Keywords
Computer Science and Digital Science
 A1.2. Networks
 A1.3.5. Cloud
 A1.3.6. Fog, Edge
 A1.6. Green Computing
 A3.4. Machine learning and statistics
 A3.5.2. Recommendation systems
 A5.2. Data visualization
 A6. Modeling, simulation and control
 A6.2.3. Probabilistic methods
 A6.2.4. Statistical methods
 A6.2.6. Optimization
 A6.2.7. High performance computing
 A8.2. Optimization
 A8.9. Performance evaluation
 A8.11. Game Theory
 A9.2. Machine learning
 A9.9. Distributed AI, Multiagent
Other Research Topics and Application Domains
 B4.4. Energy delivery
 B4.4.1. Smart grids
 B4.5.1. Green computing
 B6.2. Network technologies
 B6.2.1. Wired technologies
 B6.2.2. Radio technology
 B6.4. Internet of things
 B8.3. Urbanism and urban planning
 B9.6.7. Geography
 B9.7.2. Open data
 B9.8. Reproducibility
1 Team members, visitors, external collaborators
Research Scientists
 Arnaud Legrand [Team leader, CNRS, Senior Researcher, HDR]
 Jonatha Anselmi [Inria, Researcher]
 Nicolas Gast [Inria, Researcher, HDR]
 Bruno Gaujal [Inria, Senior Researcher, HDR]
 Patrick Loiseau [Inria, Researcher, HDR]
 Panayotis Mertikopoulos [CNRS, Researcher, HDR]
 Bary Pradelski [CNRS, Researcher]
Faculty Members
 Romain Couillet [Institut polytechnique de Grenoble, Professor, from Sep 2021]
 Vincent Danjean [Univ Grenoble Alpes, Associate Professor]
 Guillaume Huard [Univ Grenoble Alpes, Associate Professor]
 Florence Perronnin [Univ Grenoble Alpes, Associate Professor, HDR]
 JeanMarc Vincent [Univ Grenoble Alpes, Associate Professor]
 Philippe Waille [Univ Grenoble Alpes, Associate Professor]
PostDoctoral Fellows
 Henry Joseph Audeoud [INPG Entreprise SA]
 Dong Quan Vu [CNRS]
PhD Students
 Sebastian Allmeier [Inria]
 Kimon Antonakopoulos [CNRS]
 Thomas Barzola [Univ Grenoble Alpes]
 Victor Boone [École Normale Supérieure de Lyon, from Sep 2021]
 Remi Castera [Univ Grenoble Alpes, from Oct 2021]
 Tom Cornebize [Inria, until Mar 2021]
 Romain Cravic [Inria, from Oct 2021]
 Vitalii Emelianov [Inria]
 Yu Guan Hsieh [Univ Grenoble Alpes]
 Simon Philipp Jantschgi [Université de Zurich]
 Kimang Khun [Inria]
 Till Kletti [Naver Labs, CIFRE]
 Lucas Leandro Nesi [Federal University of the Rio Grande Do Sul (UFRGS), from Nov 2021]
 Hugo Lebeau [Univ Grenoble Alpes, from Oct 2021]
 Victor Leger [Univ Grenoble Alpes, from Oct 2021]
 Dimitrios Moustakas [Institut polytechnique de Grenoble]
 Louis Sebastien Rebuffi [Univ Grenoble Alpes]
 Pedro Rocha Bruel [Université de Sao Paulo  Brésil, until Oct 2021]
 Benjamin Roussillon [Univ Grenoble Alpes, until Sep 2021]
 Vera Sosnovik [Univ Grenoble Alpes]
 Chen Yan [Univ Grenoble Alpes]
Technical Staff
 Bruno De Moura Donassolo [Inria, Engineer]
 Eleni Gkiouzepi [Univ Grenoble Alpes, Engineer, until Nov 2021]
Interns and Apprentices
 Achille Baucher [Univ Grenoble Alpes, from Oct 2021]
 Victor Boone [École Normale Supérieure de Lyon, from Feb 2021 until Jul 2021]
 Remi Castera [Inria, from Apr 2021 until Sep 2021]
 Romain Cravic [Inria, from Feb 2021 until Jul 2021]
 Mael Delorme [Inria, from May 2021 until Jun 2021]
 Aurelien Gauffre [Univ Grenoble Alpes, from Feb 2021 until Jul 2021]
 Jeremy Guerin [Inria, from Apr 2021 until Sep 2021]
 Oumaima Hajji [Inria, from May 2021 until Jul 2021]
 Mathieu Molina [Inria, from May 2021 until Oct 2021]
 Julie Reynier [Inria, from May 2021 until Jul 2021]
Administrative Assistant
 Annie Simon [Inria]
2 Overall objectives
2.1 Context
Large distributed infrastructures are rampant in our society. Numerical simulations form the basis of computational sciences and high performance computing infrastructures have become scientific instruments with similar roles as those of test tubes or telescopes. Cloud infrastructures are used by companies in such an intense way that even the shortest outage quickly incurs the loss of several millions of dollars. But every citizen also relies on (and interacts with) such infrastructures via complex wireless mobile embedded devices whose nature is constantly evolving. In this way, the advent of digital miniaturization and interconnection has enabled our homes, power stations, cars and bikes to evolve into smart grids and smart transportation systems that should be optimized to fulfill societal expectations.
Our dependence and intense usage of such gigantic systems obviously leads to very high expectations in terms of performance. Indeed, we strive for lowcost and energyefficient systems that seamlessly adapt to changing environments that can only be accessed through uncertain measurements. Such digital systems also have to take into account both the users' profile and expectations to efficiently and fairly share resources in an online way. Analyzing, designing and provisioning such systems has thus become a real challenge.
Such systems are characterized by their evergrowing size, intrinsic heterogeneity and distributedness, userdriven requirements, and an unpredictable variability that renders them essentially stochastic. In such contexts, many of the former design and analysis hypotheses (homogeneity, limited hierarchy, omniscient view, optimization carried out by a single entity, openloop optimization, user outside of the picture) have become obsolete, which calls for radically new approaches. Properly studying such systems requires a drastic rethinking of fundamental aspects regarding the system's observation (measure, trace, methodology, design of experiments), analysis (modeling, simulation, trace analysis and visualization), and optimization (distributed, online, stochastic).
2.2 Objectives
The goal of the POLARIS project is to contribute to the understanding of the performance of very large scale distributed systems by applying ideas from diverse research fields and application domains. We believe that studying all these different aspects at once without restricting to specific systems is the key to push forward our understanding of such challenges and to proposing innovative solutions. This is why we intend to investigate problems arising from application domains as varied as large computing systems, wireless networks, smart grids and transportation systems.
The members of the POLARIS project cover a very wide spectrum of expertise in performance evaluation and models, distributed optimization, and analysis of HPC middleware. Specifically, POLARIS' members have worked extensively on:

Experiment design:
Experimental methodology, measuring/monitoring/tracing tools, experiment control, design of experiments, and reproducible research, especially in the context of large computing infrastructures (such as computing grids, HPC, volunteer computing and embedded systems).

Trace Analysis:
Parallel application visualization (paje, triva/viva, framesoc/ocelotl, ...), characterization of failures in large distributed systems, visualization and analysis for geographical information systems, spatiotemporal analysis of media events in RSS flows from newspapers, and others.

Modeling and Simulation:
Emulation, discrete event simulation, perfect sampling, Markov chains, Monte Carlo methods, and others.

Optimization:
Stochastic approximation, mean field limits, game theory, discrete and continuous optimization, learning and information theory.
2.3 Contribution to AI/Learning
AI and Learning is everywhere now. Let us clarify how our research activities are positionned with respect to this trend.
A first line of research in POLARIS is devoted to the use statistical learning techniques (Bayesian inference) to model the expected performance of distributed systems, to build aggregated performance views, to feed simulators of such systems, or to detect anomalous behaviours.
In a distributed context it is also essential to design systems that can seamlessly adapt to the workload and to the evolving behaviour of its components (users, resources, network). Obtaining faithful information on the dynamic of the system can be particularly difficult, which is why it is generally more efficient to design systems that dynamically learn the best actions to play through trial and errors. A key characteristic of the work in the POLARIS project is to leverage regularly gametheoretic modeling to handle situations where the resources or the decision is distributed among several agents or even situations where a centralised decision maker has to adapt to strategic users.
An important research direction in POLARIS is thus centered on reinforcement learning (Multiarmed bandits, Qlearning, online learning) and active learning in environments with one or several of the following features:
 Feedback is limited (e.g., gradient or even stochastic gradients are not available, which requires for example to resort to stochastic approximations);
 Multiagent setting where each agent learns, possibly not in a synchronised way (i.e., decisions may be taken asynchronously, which raises convergence issues);
 Delayed feedback (avoid oscillations and quantify convergence degradation);
 Non stochastic (e.g., adversarial) or non stationary workloads (e.g., in presence of shocks);
 Systems composed of a very large number of entities, that we study through mean field approximation (meanfield games and mean field control).
As a side effect, many of the gained insights can often be used to dramatically improve the scalability and the performance of the implementation of more standard machine or deep learning techniques over supercomputers.
The POLARIS members are thus particularly interested in the design and analysis of adaptive learning algorithms for multiagent systems, i.e. agents that seek to progressively improve their performance on a specific task (see Figure). The resulting algorithms should not only learn an efficient (Nash) equilibrium but they should also be able of doing so quickly (low regret), even when facing the difficulties associated to a distributed context (lack of coordination, uncertain world, information delay, limited feedback, …)
In the rest of this document, we describe in detail our new results in the above areas.
3 Research program
3.1 Performance Evaluation
Participants: Jonatha Anselmi, Vincent Danjean, Nicolas Gast, Guillaume Huard, Arnaud Legrand, Florence Perronnin, JeanMarc Vincent.
Projectteam positioning
Evaluating the scalability, robustness, energy consumption and performance of large infrastructures such as exascale platforms and clouds raises severe methodological challenges. The complexity of such platforms mandates empirical evaluation but direct experimentation via an application deployment on a realworld testbed is often limited by the few platforms available at hand and is even sometimes impossible (cost, access, early stages of the infrastructure design, etc.). Furthermore, such experiments are costly, difficult to control and therefore difficult to reproduce. Although many of these digital systems have been built by men, they have reached such a complexity level that we are no longer able to study them like artificial systems and have to deal with the same kind of experimental issues as natural sciences. The development of a sound experimental methodology for the evaluation of resource management solutions is among the most important ways to cope with the growing complexity of computing environments. Although computing environments come with their own specific challenges, we believe such general observation problems should be addressed by borrowing good practices and techniques developed in many other domains of science, in particular (1) Predictive Simulation, (2) Trace Analysis and Visualization, and (3) the Design of Experiments.
Scientific achievements
Large computing systems are particularly complex to understand because of the interplay between their discrete nature (originating from deterministic computer programs) and their stochastic nature (emerging from the physical world, long distance interactions, and complex hardware and software stacks). A first line of research in POLARIS is devoted to the design of relatively simple statistical models of key components of distributed systems and their exploitation to feed simulators of such systems, to build aggregated performance views, and to detect anomalous behaviors.
Predictive Simulation
Unlike direct experimentation via an application deployment on a realworld testbed, simulation enables fully repeatable and configurable experiments that can often be conducted quickly for arbitrary hypothetical scenarios. In spite of these promises, current simulation practice is often not conducive to obtaining scientifically sound results. To date, most simulation results in the parallel and distributed computing literature are obtained with simulators that are ad hoc, unavailable, undocumented, and/or no longer maintained. As a result, most published simulation results build on throwaway (shortlived and non validated) simulators that are specifically designed for a particular study, which prevents other researchers from building upon it. There is thus a strong need for recognized simulation frameworks by which simulation results can be reproduced, further analyzed and improved.
Many simulators of MPI applications have been developed by renowned HPC groups (e.g., at SDSC 104, BSC 49, UIUC 112, Sandia Nat. Lab. 110, ORNL 50 or ETH Zürich 80) but most of them builds on restrictive network and application modeling assumptions that generally prevent to faithfully predict execution times, which limits the use of simulation to indication of gross trends at best.
The SimGrid simulation toolkit, whose development started more than 20 years ago in UCSD, is a renowned project which gathers more than 1,700 citations and has supported the research of at least 550 articles. The most important contribution of POLARIS to this project in the last years has been to improve the quality of SimGrid to the point where it can be used effectively on a daily basis by practitioners to accurately reproduce the dynamic of real HPC systems. In particular, SMPI57, a simulator based on SimGrid that simulates unmodified MPI applications written in C/C++ or FORTRAN, has now become a very unique tool allowing to faithfully study particularly complex scenario such as legacy a legacy Geophysics application that suffers from spatial and temporal load balancing problem 83, 82 or the HPL benchmark 5637. We have shown that the performance (both for time and energy consumption 79) predicted through our simulations was systematically within a few percents of real experiments, which allows to reliably tune the applications at very low cost. This capacity has also been leveraged to study (through StarPUSimGrid) complex and modern taskbased applications running on heterogeneous sets of hybrid (CPUs + GPUs) nodes 29. The phenomenon studied through this approach would be particularly difficult to study through real experiments but yet allow to address real problems of these applications. Finally, SimGrid is also heavily used through BatSim, a batch simulator developed in the DATAMOVE team and which leverages SimGrid, to investigate the performance of machine learning strategies in a batch scheduling context 86, 113.
Trace Analysis and Visualization
Many monolithic visualization tools have been developed by renowned HPC groups since decades (e.g., BSC 97, Jülich and TU Dresden 94, 52, UIUC 78, 100, 81 and ANL 111) but most of these tools build on the classical information visualization 101 that consists in always first presenting an overview of the data, possibly by plotting everything if computing power allows, and then to allow users to zoom and filter, providing details on demand. However in our context, the amount of data comprised in such traces is several orders of magnitude larger than the number of pixels on a screen and displaying even a small fraction of the trace leads to harmful visualization artifacts. Such traces are typically made of events that occur at very different time and space scales and originate from different sources, which hinders classical approaches, especially when the application structure departs from classical MPI programs with a BSP/SMPD structure. In particular, modern HPC applications that build on a taskbased runtime and run on hybrid nodes are particularly challenging to analyze. Indeed, the underlying taskgraph is dynamically scheduled to avoid spurious synchronizations, which prevents classical visualizations to exploit and reveal the application structure.
In 65, we explain how modern data analytics tools can be used to build, from heterogeneous information sources, custom, reproducible and insightful visualizations of taskbased HPC applications at a very low development cost in the StarVZ framework. By specifying and validating statistical models of the performance of HPC applications/systems, we manage to identify when their behavior departs from what is expected and detect performance anomalies. This approach has first been applied to stateofthe art linear algebra libraries in 65 and more recently to a sparse direct solver 43. In both cases, we have been able to identify and fix several nontrivial anomalies that had not been noticed even by the application and runtime developpers. Finally, these models not only allow to reveal when applications depart from what is expected but also to summarize the execution by focusing on the most important features, which is particularly useful when comparing two execution
Design of Experiments and Reproducibility
Part of our work is devoted to the control of experiments on both classical (HPC) and novel (IoT/Fog in a smart home context) infrastructures. To this end, we heavily rely on experimental testbeds such as Grid5000 and FITIoTLab that can be wellcontrolled but real experiments are nonetheless quite resourceconsuming. Design of experiments has been successfully applied in many fields (e.g., agriculture, chemistry, industrial processes) where experiments are considered expensive. Building on concrete use cases, we explore how Design of Experiments and Reproducible Research techniques can be used to (1) design transparent autotuning strategies of scientific computation kernels 5134 (2) set up systematic performance non regression tests on Grid5000 (450 nodes for 1.5 year) and detect many abnormal events (related to bios and system upgrades, cooling, faulty memory and power unstabiliy) that had a significant effect on the nodes, from subtle performance changes of 1% to much more severe degradations of more than 10%, and had yet been unnoticed by both Grid’5000 technical team and Grid’5000 users (3) design and evaluate the performance of service provisioning strategies 458 in Fog infrastructures.
3.2 Asymptotic Methods
Participants: Jonatha Anselmi, Romain Couillet, Nicolas Gast, Bruno Gaujal, Florence Perronnin, JeanMarc Vincent.
Projectteam positioning
Stochastic models often suffer from the curse of dimensionality: their complexity grows exponentially with the number of dimensions of the system. At the same time, very large stochastic systems are sometimes easier to analyze: it can be shown that some classes of stochastic systems simplify as their dimension goes to infinity because of averaging effects such as the law of large numbers, or the central limit theorem. This form the basis of what is called an asymptotic method, which consists in studying what happens when a system gets large in order to build an approximation that is easier to study or to simulate.
Within the team, the research that we conduct in this axis is to foster the applicability of these asymptotic methods to new application areas. This lead us to work on the application of classical methods to new problems, but also to develop new approximation methods that take into account special features of the systems we study (i.e., moderate number of dimensions, transient behavior, random matrices). Typical applications are mean field method for performance evaluation, application to distributed optimization, and more recently statistical learning. One of the originality of our work is to quantify precisely what is the error made by such approximations. This allows us to define refinement terms that lead to more accurate approximations.
Scientific achievements
Refined mean field approximation
Mean field approximation is a wellknown technique in statistical physics, that was originally introduced to study systems composed of a very large number of particles (say $n>{10}^{20}$). The idea of this approximation is to assume that objects are independent and only interact between them through an average environment (the mean field). Nowadays, variants of this technique are widely applied in many domains: in game theory for instance (with the example of mean field games), but also to quantify the performance of distributed algorithms. Mean field approximation is often justified by showing a system of $n$ wellmixed interacting objects converges to its deterministic mean field approximation as $n$ goes to infinity. Yet, this does not explain why mean field approximation provides a very accurate approximation of the behavior of systems composed by a few hundreds of objects or less. Until recently, this was essentially an open question.
In 67, we give a partial answer to this question. We show that, for most of the mean field models used for performance evaluation, the error made when using a mean field approximation is a $\Theta (1/n)$. This results greatly improved compared to previous work that showed that the error made by mean field approximation was smaller than $O(1/\sqrt{n})$. On the contrary, we obtain the exact rate of accuracy. This result came from the use of Stein's method that allows one to quantify precisely the distance between two stochastic processes. Subsequently, in 69, we show that the constant in the $\Theta (1/n)$ can be computed numerically by a very efficient algorithm. By using this, we define the notion of refined approximation which consists in adding the $1/n$correction term. This methods can also be generalize to higher order extensions or 71, 66.
Design and analysis of distributed control algorithms
Mean field approximation is widely used in the perfromance evaluation community to analyze and design distributed control algorithms. Our contribution in this domain has covered mainly two applications: cache replacement algorithms and load balancing algorithms.
Cache replacement algorithms are widely used in content delivery networks. In 54, 73, 72, we show how mean field and refined mean field approximation can be used to evaluate the performance of listbased cache replacement algorithms. In particuler, we show that such policies can outperform the classically used LRU algorithm. A methological contribution of our work is that, when evaluating precisely the behavior of such a policy, the refined mean field approximation is both faster and more accurate than what could be obtain with a stochastic simulator.
Computing resources are often spread across many machines. An efficient use of such resources requires the design of a good load balancing strategy, to distribute the load among the available machines. In 47, 48, 46, we study two paradigms that we use to design asymptotically optimal load balancing policies where a central broker sends tasks to a set of parallel servers. We show in 47, 46 that combining the classical roundrobin allocation plus an evaluation of the tasks sizes can yield a policy that has a zero delay in the large system limit. This policy is interesting because the broker does not need any feedback from the servers. At the same time, this policy needs to estimate or know job durations, which is not always possible. A different approach is used in 48 where we consider a policy that does not need to estimate job durations but that uses some feedback from the servers plus a memory of where jobs where send. We show that this paradigm can also be used to design zerodelay load balancing policies as the system size grows to infinity.
Mean field games
Various notions of mean field games have been introduced in the years 20002010 in theoretical economics, engineering or game theory. A mean field game is a game in which an individual tries to maximize its utility while evolving in a population of other individuals whose behavior are not directly affected by the individual. An equilibrium is a population dynamics for which a selfish individual would behave as the population. In 60, we develop the notion of discrete space mean field games, that is more amendable to study that the previously introduced notions of mean field games. This lead to two interesting contributions: mean field games are not always the limits of stochastic games as the number of players grow 59, mean field games can be used to study how much vaccination should be subsidized to encourage people to adapt an socially optimal behaviour 18.
3.3 Distributed Online Optimization and Learning in Games
Participants: Nicolas Gast, Romain Couillet, Bruno Gaujal, Arnaud Legrand, Patrick Loiseau, Panayotis Mertikopoulos, Bary Pradelski.
Projectteam positioning
Online learning concerns the study of repeated decisionmaking in changing environments. Of course, depending on the context, the words “learning” and “decisionmaking” may refer to very different things: in economics, this could mean predicting how rational agents react to market drifts; in data networks, it could mean adapting the way packets are routed based on changing traffic conditions; in machine learning and AI applications, it could mean training a neural network or the guidance system of a selfdriving car; etc. In particular, the changes in the learner's environment could be either exogenous (that is, independent of the learner's decisions, such as the weather affecting the time of travel), or endogenous (i.e., they could depend on the learner's decisions, as in a game of poker), or any combination thereof. However, the goal for the learner(s) is always the same: to make more informed decisions that lead to better rewards over time.
The study of online learning models and algorithms dates back to the seminal work of Robbins, Nash and Bellman in the 50's, and it has since given rise to a vigorous research field at the interface of game theory, control and optimization, with numerous applications in operations research, machine learning, and data science. In this general context, our team focuses on the asymptotic behavior of online learning and optimization algorithms, both single and multiagent: whether they converge, at what speed, and/or what type of nonstationary, offequilibrium behaviors may arise when they do not.
The focus of POLARIS on gametheoretic and Markovian models of learning covers a set of specific challenges that dovetail in a highly synergistic manner with the work of other learningoriented teams within Inria (like SCOOL in Lille, SIERRA in Paris, and THOTH in Grenoble), and it is an important component of Inria's activities and contributions in the field (which includes major industrial stakeholders like Google / DeepMind, Facebook, Microsoft, Amazon, and many others).
Scientific achievements
Our team's work on online learning covers both single and multiagent models; in the sequel, we present some highlights of our work structured along these basic axes.
In the singleagent setting, an important problem in the theory of Markov decision processes – i.e., discretetime control processes with decisiondependent randomness – is the socalled “restless bandit” problem. Here, the learner chooses an action – or “arm” – from a finite set, and the mechanism determining the action's reward changes depending on whether the action was chosen or not (in contrast to standard Markov problems where the activation of an arm does not have this effect). In this general setting, Whittle conjectured – and Weber and Weiss proved – that Whittle's eponymous index policy is asymptotically optimal. However, the result of Weber and Weiss is purely asymptotic, and the rate of this convergence remained elusive for several decades. This gap was finally settled in a series of POLARIS papers 6840, where we showed that Whittle indices (as well as other index policies) become optimal at a geometric rate under the same technical conditions used by Weber and Weiss to prove Whittle's conjecture, plus a technical requirement on the nonsingularity of the fixed point of the meanfield dynamics. We also propose the first subcubic algorithm to compute Whittle and Gittins indexes. As for reinforcement learning in Markovian bandits, we have shown that Bayesian and optimistic approaches do not use the structure of Markovian bandits similarly: While Bayesian learning has both a regret and a computational complexity that scales linearly with the number of arms, optimistic approaches all incur an exponential computation time, at least in their current versions 39.
In the multiagent setting, our work has focused on the following fundamental question:
Does the concurrent use of (possibly optimal) singleagent learning algorithms
ensure convergence to Nash equilibrium in multiagent, gametheoretic environments?
Conventional wisdom might suggest a positive answer to this question because of the following “folk theorem”: under noregret learning, the agents' empirical frequency of play converges to the game's set of coarse correlated equilibria. However, the actual implications of this result are quite weak: First, it concerns the empirical frequency of play and not the daytoday sequence of actions employed by the players. Second, it concerns coarse correlated equilibria which may be supported on strictly dominated strategies – and are thus unacceptable in terms of rationalizability. These realizations prompted us to make a clean break with conventional wisdom on this topic, ultimately showing that the answer to the above question is, in general, “no”: specifically, 90, 88 showed that the (optimal) class of “followtheregularizedleader” (FTRL) learning algorithms leads to Poincaré recurrence even in simple, $2\times 2$ minmax games, thus precluding convergence to Nash equilibrium in this context.
This negative result generated significant interest in the literature as it contributed in shifting the focus towards identifying which Nash equilibria may arise as stable limit points of FTRL algorithms and dynamics. Earlier work by POLARIS on the topic 53, 91, 92 suggested that strict Nash equilibria play an important role in this question. This suspicion was recently confirmed in a series of papers 6419 where we established a sweeping negative result to the effect that mixed Nash equilibria are incompatible with noregret learning. Specifically, we showed that any Nash equilibrium which is not strict cannot be stable and attracting under the dynamics of FTRL, especially in the presence of randomness and uncertainty. This result has significant implications for predicting the outcome of a multiagent learning process because, combined with 91, it establishes the following farreaching equivalence: a state is asymptotically stable under noregret learning if and only if it is a strict Nash equilibrium.
Going beyond finite games, this further raised the question of what type of nonconvergent behaviors can be observed in continuous games – such as the class of stochastic minmax problems that are typically associated to generative adversarial networks (GANs) in machine learning. This question was one of our primary collaboration axes with EPFL, and led to a joint research project focused on the characterization of the convergence properties of zeroth, first, and (scalable) secondorder methods in nonconvex/nonconcave problems. In particular, we showed in 25 that these stateoftheart minmax optimization algorithms may converge with arbitrarily high probability to attractors that are in no way minmax optimal or even stationary – and, in fact, may not even contain a single stationary point (let alone a Nash equilibrium). Spurious convergence phenomena of this type can arise even in twodimensional problems, a fact which corroborates the empirical evidence surrounding the formidable difficulty of training GANs.
3.4 Responsible Computer Science
Participants: Nicolas Gast, Romain Couillet, Bruno Gaujal, Arnaud Legrand, Patrick Loiseau, Panayotis Mertikopoulos, Bary Pradelski.
Projectteam positioning
The topics in this axis emerge from current social and economic questions rather than from a fixed set of mathematical methods. To this end we have identified large trends such as energy efficiency, fairness, privacy, and the growing number of new market places. In addition, COVID has posed new questions that opened new paths of research with strong links to policy making.
Throughout these works, the focus of the team is on modeling aspects of the aforementioned problems, and obtaining strong theoretical results that can give highlevel guidelines on the design of markets or of decisionmaking procedures. Where relevant, we complement those works by measurement studies and audits of existing systems that allow identifying key issues. As this work is driven by topics, rather than methods, it allows for a wide range of collaborations, including with enterprises (e.g., Naverlabs), policy makers, and academics from various fields (economics, policy, epidemiology, etc.).
Other teams at Inria cover some of the societal challenges listed here (e.g., PRIVATICS, COMETE) but rather in isolation. The specificity of POLARIS resides in the breadth of societal topics covered and of the collaborations with nonCS researchers and nonresearch bodies; as well as in the application of methods such as game theory to those topics.
Scientific achievements
Algorithmic fairness
As algorithmic decisionmaking became increasingly omnipresent in our daily lives (in domains ranging from credits to advertising, hiring, or medicine); it also became increasingly apparent that the outcome of algorithms can be discriminatory for various reasons. Since 2016, the scientific community working on the problem of algorithmic fairness has been exponentially increasing. In this context, in the early days, we worked on better understanding the extent of the problem through measurement in the case of social networks 103. In particular, in this work, we showed that in advertising platforms, discrimination can occur from multiple different internal processes that cannot be controlled, and we advocate for measuring discrimination on the outcome directly. Then we worked on proposing solutions to guarantee fair representation in online public recommendations (aka trending topics on Twitter) 55. This is an example of an application in which it was observed that recommendations are typically biased towards some demographic groups. In this work, our proposed solution draws an analogy between recommendation and voting and builds on existing works on fair representation in voting. Finally, in most recent times, we worked on better understanding the sources of discrimination, in the particular simple case of selection problems, and the consequences of fixing it. While most works attribute discrimination to implicit bias of the decision maker 85, we identified a fundamentally different source of discrimination: Even in the absence of implicit bias in a decision maker’s estimate of candidates’ quality, the estimates may differ between the different groups in their variance—that is, the decision maker’s ability to precisely estimate a candidate’s quality may depend on the candidate’s group 63. We show that this differential variance leads to discrimination for two reasonable baseline decision makers (groupoblivious and Bayesian optimal). Then we analyze the consequence on the selection utility of imposing fairness mechanisms such as demographic parity or its generalization; in particular we identify some cases for which imposing fairness can improve utility. In 62, we also study similar questions in the twostage setting, and derive the optimal selector and the “price of local fairness’’ one pays in utility by imposing that the interim stage be fair.
Privacy and transparency in social computing system
Online services in general, and social networks in particular, collect massive amounts of data about their users (both online and offline). It is critical that (i) the users’ data is protected so that it cannot leak and (ii) users can know what data the service has about them and understand how it is used—this is the transparency requirement. In this context, we did two kinds of work. First, we studied social networks through measurement, in particular using the use case of Facebook. We showed that their advertising platform, through the PII1based targeting option, allowed attackers to discover some personal data of users 105. We also proposed an alternative design—valid for any system that proposed PIIbased targeting—and proved that it fixes the problem. We then audited the transparency mechanisms of the Facebook ad platform, specifically the “Ad Preferences’’ page that shows what interests the platform inferred about a user, and the “Why am I seeing this’’ button that gives some reasons why the user saw a particular ad. In both cases, we laid the foundation for defining the quality of explanations and we showed that the explanations given were lacking key desirable properties (they were incomplete and misleading, they have since been changed) 45. A followup work shed further light on the typical uses of the platform 44. In another work, we proposed an innovative protocol based on randomized withdrawal to protect public posts deletion privacy 93. Finally, in 70, we study an alternative data sharing ecosystem where users can choose the precision of the data they give. We model it as a game and show that, if users are motivated to reveal data by a public good component of the outcome’s precision, then certain basic statistical properties (the optimality of generalized least squares in particular) no longer hold.
Online markets
Market design operates at the intersection of computer science and economics and has become increasingly important as many markets are redesigned on digital platforms. Studying markets for commodities, in an ongoing project we evaluate how different fee models alter strategic incentives for both buyers and sellers. We identify two general classes of fees: for one, strategic manipulation becomes infeasible as the market grows large and agents therefore have no incentive to misreport their true valuation. On the other hand, strategic manipulation is possible and we show that in this case agents aim to maximally shade their bids. This has immediate implications for the design of such markets. By contrast, 89 considers a matching market where buyers and sellers have heterogeneous preferences over each other. Traders arrive at random to the market and the market maker, having limited information, aims to optimize when to open the market for a clearing event to take place. There is a tradeoff between thickening the market (to achieve better matches) and matching quickly (to reduce waiting time of traders in the market). The tradeoff is made explicit for a wide range of underlying preferences. These works are adding to an ongoing effort to better understand and design markets 988.
COVID
The COVID19 pandemic has put humanity to one of the defining challenges of its generation and as such naturally transdisciplinary efforts have been necessary to support decision making. In a series of articles 1096 we proposed Green Zoning. `Green zones’–areas where the virus is under control based on a uniform set of conditions–can progressively return to normal economic and social activity levels, and mobility between them is permitted. By contrast, stricter public health measures are in place in ‘red zones’, and mobility between red and green zones is restricted. France and Spain were among the first countries to introduce green zoning in April 2020. The initial success of this proposal opened up the way to a large amount of followup work analyzing and proposing various tools to effectively deploy different tools to combat the pandemic (e.g., focusmass testing 99 and a vaccination policy 95). In a joint work with a group of leading economists, public health researchers and sociologists it was found that countries that opted to aim to eliminate the virus fared better not only for public health, but also for the economy and civil liberties 9. Overall this work has been characterized by close interactions with policy makers in France, Spain and the European Commission as well as substantial activity in public discourse (via TV, newspapers and radio).
Energy efficiency
Our work on energy efficiency spanned multiple different areas and applications such as embedded systems and smart grids. Minimizing the energy consumption of embedded systems with realtime constraints is becoming more important for ecological as well as practical reasons since batteries are becoming standard power supplies. Dynamically changing the speed of the processor is the most common and efficient way to reduce energy consumption 102. In fact, this is the reason why modern processors are equipped with Dynamic Voltage and Frequency Scaling (DVFS) technology 109. In a stochastic environment, with random job sizes and arrival times, combining hard deadlines and energy minimization via DVFSbased techniques is difficult because forcing hard deadlines requires considering the worst cases, hardly compatible with random dynamics. Nevertheless, progress have been made to solve these types of problems in a series of papers using constrained Markov decision processes, both on the theoretical side (proving existence of optimal policies and showing their structure 76, 74, 75) as well as on the experimental side (showing the gains of optimal policies over classical solutions 77).
In the context of a collaboration with Enedis and Schneider Electric (via the Smart Grid chair of GrenobleINP), we also study the problem of using smart meters to optimize the behavior of electrical distribution networks. We made three kinds of contributions on this subject: (1) how to design efficient control strategies in such a system 106, 108, 107, (2) how to cosimulate an electrical network and a communication network 84, and (3) what is the performance of the communication protocol (PLC G3) used by the Linky smart meters 87.
4 Application domains
4.1 Large Computing Infrastructures
Supercomputers typically comprise thousands to millions of multicore CPUs with GPU accelerators interconnected by complex interconnection networks that are typically structured as an intricate hierarchy of network switches. Capacity planning and management of such systems not only raises challenges in term of computing efficiency but also in term of energy consumption. Most legacy (SPMD) applications struggle to benefit from such infrastructure since the slightest failure or load imbalance immediately causes the whole program to stop or at best to waste resources. To scale and handle the stochastic nature of resources, these applications have to rely on dynamic runtimes that schedule computations and communications in an opportunistic way. Such evolution raises challenges not only in terms of programming but also in terms of observation (complexity and dynamicity prevents experiment reproducibility, intrusiveness hinders large scale data collection, ...) and analysis (dynamic and flexible application structures make classical visualization and simulation techniques totally ineffective and require to build on ad hoc information on the application structure).
4.2 NextGeneration Wireless Networks
Considerable interest has arisen from the seminal prediction that the use of multipleinput, multipleoutput (MIMO) technologies can lead to substantial gains in information throughput in wireless communications, especially when used at a massive level. In particular, by employing multiple inexpensive service antennas, it is possible to exploit spatial multiplexing in the transmission and reception of radio signals, the only physical limit being the number of antennas that can be deployed on a portable device. As a result, the wireless medium can accommodate greater volumes of data traffic without requiring the reallocation (and subsequent reregulation) of additional frequency bands. In this context, throughput maximization in the presence of interference by neighboring transmitters leads to games with convex action sets (covariance matrices with trace constraints) and individually concave utility functions (each user's Shannon throughput); developing efficient and distributed optimization protocols for such systems is one of the core objectives of Theme 5.
Another major challenge that occurs here is due to the fact that the efficient physical layer optimization of wireless networks relies on perfect (or close to perfect) channel state information (CSI), on both the uplink and the downlink. Due to the vastly increased computational overhead of this feedback – especially in decentralized, smallcell environments – the ongoing transition to fifth generation (5G) wireless networks is expected to go handinhand with distributed learning and optimization methods that can operate reliably in feedbackstarved environments. Accordingly, one of POLARIS' applicationdriven goals will be to leverage the algorithmic output of Theme 5 into a highly adaptive resource allocation framework for nextgéneration wireless systems that can effectively "learn in the dark", without requiring crippling amounts of feedback.
4.3 Energy and Transportation
Smart urban transport systems and smart grids are two examples of collective adaptive systems. They consist of a large number of heterogeneous entities with decentralised control and varying degrees of complex autonomous behaviour. We develop an analysis tools to help to reason about such systems. Our work relies on tools from fluid and meanfield approximation to build decentralized algorithms that solve complex optimization problems. We focus on two problems: decentralized control of electric grids and capacity planning in vehiclesharing systems to improve load balancing.
4.4 Social Computing Systems
Social computing systems are online digital systems that use personal data of their users at their core to deliver personalized services directly to the users. They are omnipresent and include for instance recommendation systems, social networks, online medias, daily apps, etc. Despite their interest and utility for users, these systems pose critical challenges of privacy, security, transparency, and respect of certain ethical constraints such as fairness. Solving these challenges involves a mix of measurement and/or audit to understand and assess issues, and modeling and optimization to propose and calibrate solutions.
5 Social and environmental responsibility
5.1 Footprint of research activities
The carbon footprint of the team has been quite minimal in 2021 since there has been no travel allowed with most of us working from home. Our team does not train heavy ML models requiring important processing power although some of us perform computer science experiments, mostly using the Grid5000 platforms. We keep this usage very reasonable and rely on cheaper alternatives (e.g., simulations) as much as possible.
Along this line, an interesting initiative lies in the PhD work of Tom Cornebize 33 who evaluated the carbon footprint of this thesis. The total amount of greenhouse gas emissions of this thesis due to airplane transportation is 7.6 t of CO2eq and he estimates that the total amount of greenhouse gas emissions of this thesis due to computing is 10.6 t of CO2eq (a total of 2,112,014 core hours on Grid5000). The initial goal of the thesis was to evaluate (and possibly improve) the reliability of SimGrid to predict the performance of an MPI application like HPL. About 10% have been devoted to running SMPI simulations (to obtain predictions), 30% to run MPI applications (so as to compare the predictions with real executions), and 60% for a systematic performance measurement of a dozen of Grid5000 clusters over a long period of time (over two years). We are still unsure about whether this last part was worth the cost but this long and largescale measurement was motivated by the need to characterize the variability of modern platforms, which is documented but largely underestimated by observational studies. Although we made our best to decrease the cost of this experiment from the start and proceeded gradually, the overall cost remains high. This study raises the question of the responsibility of the verification of the platform state (user vs. administrator) and we expect the lessons learned will be useful to the community.
5.2 Sens Workshop
On November 19th, a Sens Workshop was held, organized within the Inria DataMove and Polaris teams. We were ten participants. All participants were permanent members of one of the two teams. Participation in the workshop was on a voluntary basis. The day's proceedings followed four main axes: (1) Why do you do research? (2) Construction of a map of the expectations of everyone in the team. (3) Selection of two texts to be read and exchange around questions about the goal of research; (3) Prospective.
The first axe took place mainly in small groups. We were interested in why we work in the academic world and why this subject. It emerged that the motivations are very varied (ranging from intellectual curiosity to the desire to change the world), as well as the desire of several participants to change their object of study. The second session aimed to map the goals and constraints that bind us to our profession as researchers and to organize these different themes into a mural. Rigorous scientific production and education seem to be at the center of our priorities, while a question remains about the lack of group emulation and the too great part of individualism (and competition) in the current academic world. The last axes were the occasion to exchange around several texts on the impact of our profession of researcher in the current digital world, in particular linked to the fact that digital technology deeply modifies human activities and relationships, with a strong societal and environmental impact.
Without taking a concrete direction, this day was rich in learning. We think that it will be followed by other days of this type in the future.
5.3 Raising awareness on the climate crisis
Romain Couillet has organized several introductory seminars on the Anthropocene, which he has presented to students at the UGA and GrenobleINP, as well as to associations in Grenoble (FNE, AgirAlternatif). He is also coresponsible of the Digital Transformation DU. He has published three articles on the issue of "usability" of artificial intelligence, and is the organizer of a special session on "Signal processing and resilience" for the GRETSI 2022 conference. He is also cocreator of the sustainable AI transversal axis of the MIAI project in Grenoble. Finally, he is a trainer for the "Fresque du Climat" and a member of Adrastia and FNE Isère.
5.4 Impact of research results
The efforts of B. Pradelski on COVID policy has received lots of media coverage in Le Monde and other major newspapers. See Section 11.3 for more details.
6 Highlights of the year
6.1 Awards
 R. Couillet has received the IEEE/SEE Prix Glavieux 2021 for his work on large dimension statistics for artificial intelligence.
 Y.P. Hsieh, P. Mertikopoulos, and V. Cevher have been accepted for a long talk to present their work on The limits of minmax optimization algorithms: Convergence to spurious noncritical sets at ICML 2021 25.
 L. Nesi, A. Legrand, and L. Schnorr have received a best paper paward from the ICPP'21 conference for their work on Exploiting system level heterogeneity to improve the performance of a GeoStatistics multiphase taskbased application29.
7 New software and platforms
7.1 New software
7.1.1 SimGrid

Keywords:
Largescale Emulators, Grid Computing, Distributed Applications

Scientific Description:
SimGrid is a toolkit that provides core functionalities for the simulation of distributed applications in heterogeneous distributed environments. The simulation engine uses algorithmic and implementation techniques toward the fast simulation of large systems on a single machine. The models are theoretically grounded and experimentally validated. The results are reproducible, enabling better scientific practices.
Its models of networks, cpus and disks are adapted to (Data)Grids, P2P, Clouds, Clusters and HPC, allowing multidomain studies. It can be used either to simulate algorithms and prototypes of applications, or to emulate real MPI applications through the virtualization of their communication, or to formally assess algorithms and applications that can run in the framework.
The formal verification module explores all possible message interleavings in the application, searching for states violating the provided properties. We recently added the ability to assess liveness properties over arbitrary and legacy codes, thanks to a systemlevel introspection tool that provides a finely detailed view of the running application to the model checker. This can for example be leveraged to verify both safety or liveness properties, on arbitrary MPI code written in C/C++/Fortran.

Functional Description:
SimGrid is a toolkit that provides core functionalities for the simulation of distributed applications in heterogeneous distributed environments. The simulation engine uses algorithmic and implementation techniques toward the fast simulation of large systems on a single machine. The models are theoretically grounded and experimentally validated. The results are reproducible, enabling better scientific practices.
Its models of networks, cpus and disks are adapted to (Data)Grids, P2P, Clouds, Clusters and HPC, allowing multidomain studies. It can be used either to simulate algorithms and prototypes of applications, or to emulate real MPI applications through the virtualization of their communication, or to formally assess algorithms and applications that can run in the framework.
The formal verification module explores all possible message interleavings in the application, searching for states violating the provided properties. We recently added the ability to assess liveness properties over arbitrary and legacy codes, thanks to a systemlevel introspection tool that provides a finely detailed view of the running application to the model checker. This can for example be leveraged to verify both safety or liveness properties, on arbitrary MPI code written in C/C++/Fortran.

News of the Year:
There were 3 major releases in 2021. A new API was introduced to create the platform descriptions directly from the source code instead of XML, providing much more expressiveness to the experimenters. SMPI now reports memory leaks and correctly diagnoses API misuses, which makes it even more adapted to teaching settings. The documentation was thoroughly overhauled to ease the use of the framework. We also pursued our efforts to improve the overall framework, through bug fixes, code refactoring and other software quality improvement.
 URL:

Contact:
Martin Quinson

Participants:
Adrien Lebre, AnneCécile Orgerie, Arnaud Legrand, Augustin Degomme, Emmanuelle Saillard, Frédéric Suter, JeanMarc Vincent, Jonathan Pastor, Luka Stanisic, Martin Quinson, Samuel Thibault

Partners:
CNRS, ENS Rennes
7.1.2 PSI

Name:
Perfect Simulator

Keywords:
Markov model, Simulation

Functional Description:
Perfect simulator is a simulation software of markovian models. It is able to simulate discrete and continuous time models to provide a perfect sampling of the stationary distribution or directly a sampling of functional of this distribution by using coupling from the past. The simulation kernel is based on the CFTP algorithm, and the internal simulation of transitions on the Aliasing method.

News of the Year:
No active development. Maintenance is ensured by the POLARIS team. The next generation of PSI lies in the MARTO project.
 URL:

Contact:
JeanMarc Vincent
7.1.3 marmoteCore

Name:
Markov Modeling Tools and Environments  the Core

Keywords:
Modeling, Stochastic models, Markov model

Functional Description:
marmoteCore is a C++ environment for modeling with Markov chains. It consists in a reduced set of highlevel abstractions for constructing state spaces, transition structures and Markov chains (discretetime and continuoustime). It provides the ability of constructing hierarchies of Markov models, from the most general to the particular, and equip each level with specifically optimized solution methods.
This software was started within the ANR MARMOTE project: ANR12MONU00019.

News of the Year:
No active development. Current development lies now in the MARTO project (next generations of PSI and marmoteCore) and in the forthcoming Marmote project.
 URL:
 Publications:

Contact:
Alain JeanMarie

Participants:
Alain JeanMarie, Hlib Mykhailenko, Benjamin Briot, Franck Quessette, Issam Rabhi, JeanMarc Vincent, JeanMichel Fourneau

Partners:
Université de Versailles StQuentinenYvelines, Université Paris Nanterre
7.1.4 MarTO

Name:
Markov Toolkit for Markov models simulation: perfect sampling and Monte Carlo simulation

Keywords:
Perfect sampling, Markov model

Functional Description:
MarTO is a simulation software of markovian models. It is able to simulate discrete and continuous time models to provide a perfect sampling of the stationary distribution or directly a sampling of functional of this distribution by using coupling from the past. The simulation kernel is based on the CFTP algorithm, and the internal simulation of transitions on the Aliasing method. This software is a rewrite, more efficient and flexible, of PSI

News of the Year:
No official release yet. The code development is in progress.
 URL:

Contact:
Vincent Danjean
7.1.5 GameSeer

Keyword:
Game theory

Functional Description:
GameSeer is a tool for students and researchers in game theory that uses Mathematica to generate phase portraits for normal form games under a variety of (usercustomizable) evolutionary dynamics. The whole point behind GameSeer is to provide a dynamic graphical interface that allows the user to employ Mathematica's vast numerical capabilities from a simple and intuitive frontend. So, even if you've never used Mathematica before, you should be able to generate fully editable and customizable portraits quickly and painlessly.

News of the Year:
No new release but the development is still active.
 URL:

Contact:
Panayotis Mertikopoulos
7.1.6 rmf_tool

Name:
A library to Compute (Refined) Mean Field Approximations

Keyword:
Mean Field

Functional Description:
The tool accepts three model types:
 homogeneous population processes (HomPP)  density dependent population processes (DDPPs)  heterogeneous population models (HetPP)
In particular, it provides a numerical algorithm to compute the constant of the "refined mean field approximation" provided in the paper A Refined Mean Field Approximation by N. Gast and B. Van Houdt, accepted at SIGMETRICS 2018. And a framework to compute heterogeneous mean field approximations Mean Field and Refined Mean Field Approximations for Heterogeneous Systems: It Works! by N. Gast and S. Allmeier, accepted at SIGMETRICS 2022.
 URL:
 Publications:

Contact:
Nicolas Gast
8 New results
The new results produced by the team in 2020 can be grouped into the following categories.
8.1 HPC application analysis and optimization
Participants: Tom Cornebize, Vincent Danjean, Arnaud Legrand, Lucas Leandro Nesi, JeanMarc Vincent.
Finely tuning applications and understanding the influence of key parameters (number of processes, granularity, collective operation algorithms, virtual topology, and process placement) is critical to obtain good performance on supercomputers. With the high consumption of running applications at scale, doing so solely to optimize their performance is particularly costly. We have shown in 37 that SimGrid and SMPI could be used to obtain inexpensive but faithful predictions of expected performance. The methodology we propose decouples the complexity of the platform, which is captured through statistical models of the performance of its main components (MPI communications, BLAS operations), from the complexity of adaptive applications by emulating the application and skipping regular nonMPI parts of the code. We demonstrate the capability of our method with HighPerformance Linpack (HPL), the benchmark used to rank supercomputers in the TOP500, which requires careful tuning. This work presents an extensive (in)validation study that compares simulation with real experiments and demonstrates our ability to predict the performance of HPL within a few percent consistently. This study allows us to identify the main modeling pitfalls (e.g., spatial and temporal node variability or network heterogeneity and irregular behavior) that need to be considered. Our “surrogate” also allows studying several subtle HPL parameter optimization problems while accounting for uncertainty on the platform. This work is part of the PhD work of Tom Cornebize 33 and the spatial and temporal node variability has also been investigated and quantified through a systematically measurement of the performance of more than 450 nodes from a dozen of clusters of the Grid’5000 testbed for two years using a rigorous experimental discipline. Using a simple statistical test, we managed to detect many performance changes, from subtle ones of 1% to much more severe degradation of more than 10%, but which could significantly impact the outcome of experiments. The root cause behind detected performance changes ranges from BIOS and system upgrades to cooling issues, faulty memory, and power instability. These events went unnoticed by both Grid’5000 technical team and Grid’5000 users, yet they could greatly harm the reproducibility of experiments and lead to wrong scientific conclusions. All this work heavily builds on reproducible research methodology: the data and metadata collected for this work are permanently and publicly archived under an open license2 and presented at through a collection of Jupyter notebooks at cornebize.net/g5k_test/.Overall, over the last few years, the quality of SimGrid predictions for HPC applications has reach an unprecedented quality, which allows investigating and optimizing the performance of complex applications in a very controled and reproducible yet realistic way. In 29, we study ExaGeoStat, a taskbased machine learning framework specifically designed for geostatistics data. Every iteration of this application comprises several phases that do not scale in the same way, which makes the load particularly challenging to balance. In this work, we show how such applications with multiple phases with distinct resource necessities can take advantage of internode heterogeneity to improve performance and reduce resource idleness. We first show how to improve application phase overlap by optimizing runtime and scheduling decisions and then how to compute the optimal distribution for all the phases using a linear program leveraging node heterogeneity while limiting communication overhead. The performance gains of our phase overlap improvements are between 36% and 50% compared to the original base synchronous and homogeneous execution. We show that by adding some slow nodes to a homogeneous set of fast nodes, we can improve the performance by another 25% compared to a standard blockcyclic distribution, thereby harnessing any machine. Most of these algorithmic and scheduling improvements have been investigated in simulation with StarPUSimGrid as it allows for controled tracing and debugging on specific platform configurations before being confirmed through real experiments on real testbeds such as Grid 5000 and Santos Dumont.
Finally, we have shown in 43 how the structure of complex applications such as a multifrontal sparse linear solvers could be exploited to detect and correct nontrivial performance problems. Efficiently exploiting computational resources in heterogeneous platforms is a real challenge which has motivated the adoption of the taskbased programming paradigm where resource usage is dynamic and adaptive. Unfortunately, classical performance visualization techniques used in routine performance analysis often fail to provide any insight in this new context, especially when the application structure is irregular. We propose and implement in StarVZ several performance visualization techniques tailored for the analysis of taskbased multifrontal sparse linear solvers and show that by building on both a performance model of irregular tasks and on structure of the application (in particular the elimination tree), we can detect and highlight anomalies and understand resource utilization from the application pointofview in a very insightful way. We validate these novel performance analysis techniques with the QR_mumps sparse parallel solver by describing a series of case studies where we identify and address non trivial performance issues thanks to our visualization methodology.
8.2 Large system analysis and optimization
Participants: Jonatha Anselmi, Nicolas Gast, Olivier Bilenne, Sebastian Allmeier, JeanMarc Vincent.
Large systems can be (1) particularly difficult to analyze because of inherent statespace explosion and (2) require robust and scalable scheduling techniques. In this series of work, we contribute to a better understanding of both aspects.
In 6, we study the impact of communication latency on the classical Work Stealing load balancing algorithm by extending the reference model. By using a theoretical analysis and simulation, we study the overall impact of latency on the Makespan (maximum completion time) and we derive a new expression of the expected running time of a bag of independent tasks scheduled by Work Stealing. This expression enables us to predict under which conditions a given run will yield acceptable performance. For instance, we can easily calibrate the maximal number of processors to use for a given work/platform combination. All our results are validated through simulation on a wide range of parameters.
A complementary approach to work stealing in such system is replication but it is a doubleedged weapon that must be handled with caution as the resource overhead may be detrimental when used too aggressively. In 1, we provide a queueingtheoretic framework for job replication schemes based on the principle "replicate a job as soon as the system detects it as a straggler". This is called job speculation. Recent works have analyzed replication on arrival, which we refer to as replication. Replication is motivated by its implementation in Google's BigTable. However, systems such as Apache Spark and Hadoop MapReduce implement speculative job execution. The performance and optimization of speculative job execution is not well understood. To this end, we propose a queueing network model for load balancing where each server can speculate on the execution time of a job. Specifically, each job is initially assigned to a single server by a frontend dispatcher. Then, when its execution begins, the server sets a timeout. If the job completes before the timeout, it leaves the network, otherwise the job is terminated and relaunched or resumed at another server where it will complete. We provide a necessary and sufficient condition for the stability of speculative queueing networks with heterogeneous servers, general job sizes and scheduling disciplines. We find that speculation can increase the stability region of the network when compared with standard load balancing models and replication schemes. We provide general conditions under which timeouts increase the size of the stability region and derive a formula for the optimal speculation time, i.e., the timeout that minimizes the load induced through speculation. We compare speculation with redundantd and redundanttoidlequeued rules under an S&X model. For light loaded systems, redundancy schemes provide better response times. However, for moderate to heavy loadings, redundancy schemes can lose capacity and have markedly worse response times when compared with the proposed speculative scheme.
A key challenge in such systems comes from the structure and from the high variability of the execution time distribution. We also study the dispatching to parallel servers problem in 2 where we seek to minimize the average cost experienced by the system over an infinite time horizon. A standard approach for solving this problem is through policy iteration techniques, which relies on the computation of value functions. In this context, we consider the continuousspace $M/G/1FCFS$ queue endowed with an arbitrarilydesigned cost function for the waiting times of the incoming jobs. The associated relative value function is a solution of Poisson's equation for Markov chains, which in this work we solve in the Laplace transform domain by considering an ancillary, underlying stochastic process extended to (imaginary) negative backlog states. This construction enables us to issue closedform relative value functions for polynomial and exponential cost functions and for piecewise compositions of the latter, in turn permitting the derivation of interval bounds for the relative value function in the form of power series or trigonometric sums. We review various cost approximation schemes and assess the convergence of the interval bounds these induce on the relative value function. Namely: Taylor expansions (divergent, except for a narrow class of entire functions with low orders of growth), and uniform approximation schemes (polynomials, trigonometric), which achieve optimal convergence rates over finite intervals. This study addresses all the steps to implementing dispatching policies for systems of parallel servers, from the specification of general cost functions towards the computation of interval bounds for the relative value functions and the exact implementation of the firstpolicy improvement step.
Finally, when the number of entities is large, most computations are untractable but mean field approximation is a powerful technique to study the performance of very large stochastic systems represented as systems of interacting objects. Applications include load balancing models, epidemic spreading, cache replacement policies, or largescale data centers, for which mean field approximation gives very accurate estimates of the transient or steadystate behaviors. In a series of recent papers, a new and more accurate approximation, called the refined mean field approximation has been presented. A key strength of this technique lies in its applicability to notsolarge systems. Yet, computing this new approximation can be cumbersome. In 13, we present a tool, called rmf tool and available at github.com/ngast/rmf_tool, that takes the description of a mean field model, and can numerically compute its mean field approximations and refinement.
8.3 Energy optimization
Participants: Jonatha Anselmi, Bruno Gaujal, Panayotis Mertikopoulos, Stéphan Plassart, LouisSébastien Rebuffi.
Energy consumption is a major concern in modern architectures. In 7, we consider the classical problem of minimizing offline the total energy consumption required to execute a set of n realtime jobs on a single processor with a finite number of available speeds. Each realtime job is defined by its release time, size, and deadline (all bounded integers). The goal is to find a processor speed schedule, such that no job misses its deadline and the energy consumption is minimal. We propose a pseudolinear time algorithm that checks the schedulability of the given set of n jobs and computes an optimal speed schedule. The time complexity of our algorithm is in $O\left(n\right)$, to be compared with $O(nlog(n\left)\right)$ for the best known solution. Besides the complexity gain, the main interest of our algorithm is that it is based on a completely different idea: instead of computing the critical intervals, it sweeps the set of jobs and uses a dynamic programming approach to compute an optimal speed schedule. Our linear time algorithm is still valid (with some changes) when arbitrary (nonconvex) power functions and when switching costs are taken into account.
In 36, we consider this problem in a dynamic setting where a Dynamic Voltage and Frequency Scaling (DVFS) processor should execute jobs with obsolescence deadlines: A job becomes obsolete and is removed from the system if it is not completed before its deadline. The objective is to design a dynamic speed policy for the processor that minimizes its average energy consumption plus an obsolescence cost per deadline miss. Under Poisson arrivals and exponentially distributed deadlines and job sizes, we show that this problem can be modeled as a continuous time Markov decision process (MDP) with unbounded state space and unbounded rates. While this MDP admits a continuous time optimality equation for its average cost, the standard uniformization approach is not applicable. Inspired by the scaling method introduced by Blok and Spieksma, we first define a family of truncated MDPs and we then show that the optimal speed profiles are increasing in the number of jobs in the system and are uniformly bounded by a constant. Finally, we show that these properties are inherited from the original (infinite) system. The proposed upper bound on the optimal speed profile is tight and is used to develop an extremely simple policy that accurately approximates the optimal average cost in heavy traffic conditions.
Finally, we study power management in a distributed and online context in 12 through learning and game design. We consider the targetrate power management problem for wireless networks and we propose two simple, distributed power management schemes that regulate power in a provably robust manner by efficiently leveraging past information. Both schemes are obtained via a combined approach of learning and “game design” where we (1) design a game with suitable payoff functions such that the optimal joint power profile in the original power management problem is the unique Nash equilibrium of the designed game; and (2) derive distributed power managment algorithms by directing the networks' users to employ a noregret learning algorithm to maximize their individual utility over time. To establish convergence, we focus on the wellknown online eager gradient descent learning algorithm in the class of weighted strongly monotone games. In this class of games, we show that when players only have access to imperfect stochastic feedback, multiagent online eager gradient descent converges to the unique Nash equilibrium in mean square at an $O(1/T)$ rate. In the context of power management in static networks, we show that the designed games are weighted strongly monotone if the network is feasible (i.e. when all users can concurrently attain their target rates). This allows us to derive geometric convergence rate to the joint optimal transmission power. More importantly, in stochastic networks where channel quality fluctuates over time, the designed games are also weighted strongly monotone and the proposed algorithms converge in mean square to the joint optimal transmission power at a $O(1/T)$ rate, even when the network is only feasible on average (i.e. users may be unable to meet their requirements with positive probability). This comes in stark contrast to existing algorithms (like the seminal Foschini–Miljanic algorithm and its variants) that may fail to converge altogether.
8.4 Learning in time varying systems
Participants: Yu Guan Hsieh, Panayotis Mertikopoulos, Barry Pradelski, Patrick Loiseau.
Some form of stationarity and time synchronism is generally required to guarantee the efficiency of distributed algorithms in large systems. In this series of work, we work on releasing some of these properties.One of the most widely used methods for solving largescale stochastic optimization problems is distributed asynchronous stochastic gradient descent (DASGD), a family of algorithms that result from parallelizing stochastic gradient descent on distributed computing architectures (possibly) asychronously. However, a key obstacle in the efficient implementation of DASGD is the issue of delays: when a computing node contributes a gradient update, the global model parameter may have already been updated by other nodes several times over, thereby rendering this gradient information stale. These delays can quickly add up if the computational throughput of a node is saturated, so the convergence of DASGD may be compromised in the presence of large delays. In 11, we show that, by carefully tuning the algorithm's stepsize, convergence to the critical set is still achieved in mean square, even if the delays grow unbounded at a polynomial rate. We also establish finer results in a broad class of structured optimization problems (called variationally coherent), where we show that DASGD converges to a global optimum with probability 1 under the same delay assumptions. Together, these results contribute to the broad landscape of largescale nonconvex stochastic optimization by offering stateoftheart theoretical guarantees and providing insights for algorithm design.
In 42, we provide a general framework for studying multiagent online learning problems in the presence of delays and asynchronicities. Specifically, we propose and analyze a class of adaptive dual averaging schemes in which agents only need to accumulate gradient feedback received from the whole system, without requiring any betweenagent coordination. In the singleagent case, the adaptivity of the proposed method allows us to extend a range of existing results to problems with potentially unbounded delays between playing an action and receiving the corresponding feedback. In the multiagent case, the situation is significantly more complicated because agents may not have access to a global clock to use as a reference point; to overcome this, we focus on the information that is available for producing each prediction rather than the actual delay associated with each feedback. This allows us to derive adaptive learning strategies with optimal regret bounds, even in a fully decentralized, asynchronous environment. Finally, we also analyze an "optimistic" variant of the proposed algorithm which is capable of exploiting the predictability of problems with a slower variation and leads to improved regret bounds.
We also use the dual averaging technique in 24, where we address an open network (agents can join and leave the network at any time) context. In networks of autonomous agents (e.g., fleets of vehicles, scattered sensors), the problem of minimizing the sum of the agents' local functions has received a lot of interest. Leveraging recent online optimization techniques, we propose and analyze the convergence of a decentralized asynchronous optimization method for open networks.
Finally, we examine in 38 and 27 the longrun behavior of multiagent online learning in games that evolve over time. Specifically, we examine the equilibrium tracking and convergence properties of noregret learning algorithms in continuous games that evolve over time. We focus on learning via "mirror descent", a widely used class of noregret learning schemes where players take small steps along their individual payoff gradients and then "mirror" the output back to their action sets, and we show that the induced sequence of play (a) converges to Nash equilibrium in timevarying games that stabilize in the long run to a strictly monotone limit; and (b) it stays asymptotically close to the evolving equilibrium of the sequence of stage games (assuming they are strongly monotone). Our results apply to both gradientbased and payoffbased feedback, i.e., the "bandit" case where players only observe the payoffs of their chosen actions.
8.5 Advanced learning methods
Participants: Kimon Antonakopoulos, Yu Guan Hsieh, Panayotis Mertikopoulos, Bary Pradelski.
Variational inequalities – and, in particular, stochastic variational inequalities – have recently attracted considerable attention in machine learning and learning theory as a flexible paradigm for "optimization beyond minimization", i.e., for problems where finding an optimal solution does not necessarily involve minimizing a loss function.
In 17, we analyze the convergence rate of optimistic mirror descent methods in stochastic variational inequalities. Our analysis reveals an intricate relation between the algorithm's rate of convergence and the local geometry induced by the method's underlying Bregman function. We quantify this relation by means of the Legendre exponent, a notion that we introduce to measure the growth rate of the Bregman divergence relative to the ambient norm near a solution. We show that this exponent determines both the optimal stepsize policy of the algorithm and the optimal rates attained, explaining in this way the differences observed for some popular Bregman functions (Euclidean projection, negative entropy, fractional power, etc.).
3, we develop a new stochastic algorithm for solving pseudomonotone stochastic variational inequalities. Our method builds on Tseng’s forwardbackward forward (FBF) algorithm, which is known in the deterministic literature to be a valuable alternative to Korpelevich’s extragradient method when solving variational inequalities over a convex and closed set governed by pseudomonotone, Lipschitz continuous operators. The main computational advantage of Tseng’s algorithm is that it relies only on a single projection step and two independent queries of a stochastic oracle. Our algorithm incorporates a minibatch sampling mechanism and leads to almost sure (a.s.) convergence to an optimal solution. To the best of our knowledge, this is the first stochastic lookahead algorithm achieving this by using only a single projection at each iteration.
In 16, we examine a flexible algorithmic framework for solving monotone variational inequalities in the presence of randomness and uncertainty. The proposed template encompasses a wide range of popular firstorder methods, including dual averaging, dual extrapolation and optimistic gradient algorithms – both adaptive and nonadaptive. Our first result is that the algorithm achieves the optimal rates of convergence for cocoercive problems when the profile of the randomness is known to the optimizer: $O(1/\sqrt{T})$ for absolute noise profiles, and $O(1/T)$ for relative ones. Subsequently, we drop all prior knowledge requirements (the absolute/relative variance of the randomness affecting the problem, the operator's cocoercivity constant, etc.), and we analyze an adaptive instance of the method that gracefully interpolates between the above rates, i.e., it achieves $O(1/\sqrt{T})$ and $O(1/T)$ in the absolute and relative cases, respectively. To our knowledge, this is the first universality result of its kind in the literature and, somewhat surprisingly, it shows that an extragradient proxy step is not required to achieve optimal rates.
An other challenging and promising problem motivated by applications in machine learning and operations research is stochastic regret minimization in nonconvex problems:
In 21, we study regret regret minimization with stochastic firstorder oracle feedback in online constrained, and possibly nonsmooth, nonconvex problems. In this setting, the minimization of external regret is beyond reach, so we focus on a local regret measure defined via a proximalgradient mapping. To achieve no (local) regret in this setting, we develop a proxgrad method based on stochastic firstorder feedback, and a simpler method for when access to a perfect firstorder oracle is possible. Both methods are minmax orderoptimal, and we also establish a bound on the number of proxgrad queries these methods require. As an important application of our results, we also obtain a link between online and offline nonconvex stochastic optimization manifested as a new proxgrad scheme with complexity guarantees matching those obtained via variance reduction techniques.
In 22, we propose a hierarchical version of dual averaging for zerothorder online nonconvex optimizationi.e., learning processes where, at each stage, the optimizer is facing an unknown nonconvex loss function and only receives the incurred loss as feedback. The proposed class of policies relies on the construction of an online model that aggregates loss information as it arrives, and it consists of two principal components: (a) a regularizer adapted to the Fisher information metric (as opposed to the metric norm of the ambient space); and (b) a principled exploration of the problem's state space based on an adapted hierarchical schedule. This construction enables sharper control of the model's bias and variance, and allows us to derive tight bounds for both the learner's static and dynamic regreti.e., the regret incurred against the best dynamic policy in hindsight over the horizon of play.
8.6 Adaptive algorithms
Participants: Kimon Antonakopoulos, Yu Guan Hsieh, Panayotis Mertikopoulos, Dong Quan Vu.
Designing algorithms that perform well in a variety of regime is particularly challenging. In a series of work, we study how to get the best of both worlds in a variety of contexts:
In 30, we examine an adaptive learning framework for nonatomic congestion games where the players' cost functions may be subject to exogenous fluctuations (e.g., due to disturbances in the network, variations in the traffic going through a link). In this setting, the popular multiplicative/ exponential weights algorithm enjoys an $O(1/\sqrt{T})$ equilibrium convergence rate. However, this rate is suboptimal in static environments, i.e., when the network is not subject to randomness. In this static regime, accelerated algorithms achieve an $O(1/{T}^{2})$ convergence speed, but they fail to converge altogether in stochastic problems. To fill this gap, we propose a novel, adaptive exponential weights method that seamlessly interpolates between the $O(1/{T}^{2})$ and $O(1/\sqrt{T})$ in the static and stochastic regimes respectively. Importantly, this "bestofbothworlds" guarantee does not require any prior knowledge of the problem's parameters or tuning by the optimizer. In addition, the method's convergence speed depends subquadratically on the size of the network (number of vertices and edges), so it scales gracefully to large, reallife urban networks.
In 14, we present a new family of minmax optimization algorithms that automatically exploit the geometry of the gradient data observed at earlier iterations to perform more informative extragradient steps in later ones. Thanks to this adaptation mechanism, the proposed method automatically detects whether the problem is smooth or not, without requiring any prior tuning by the optimizer. As a result, the algorithm simultaneously achieves orderoptimal convergence rates, i.e., it converges to an εoptimal solution within O(1/ε) iterations in smooth problems, and within O(1/ε 2) iterations in nonsmooth ones. Importantly, these guarantees do not require any of the standard boundedness or Lipschitz continuity conditions that are typically assumed in the literature; in particular, they apply even to problems with singularities (such as resource allocation problems and the like). This adaptation is achieved through the use of a geometric apparatus based on Finsler metrics and a suitably chosen mirrorprox template that allows us to derive sharp convergence rates for the methods at hand.
In 15, we propose a new family of adaptive firstorder methods for a class of convex minimization problems that may fail to be Lipschitz continuous or smooth in the standard sense. Specifically, motivated by a recent flurry of activity on nonLipschitz (NoLips) optimization, we consider problems that are continuous or smooth relative to a reference Bregman functionas opposed to a global, ambient norm (Euclidean or otherwise). These conditions encompass a wide range of problems with singular objective, such as Fisher markets, Poisson tomography, Ddesign, and the like. In this setting, the application of existing orderoptimal adaptive methodslike UnixGrad or AcceleGradis not possible, especially in the presence of randomness and uncertainty. The proposed method, adaptive mirror descent (AdaMir), aims to close this gap by concurrently achieving minmax optimal rates in problems that are relatively continuous or smooth, including stochastic ones.
Finally, we study how such noregret strategies fare in a multiagent context. In gametheoretic learning, several agents are simultaneously following their individual interests, so the environment is nonstationary from each player's perspective. In this context, the performance of a learning algorithm is often measured by its regret. However, noregret algorithms are not created equal in terms of gametheoretic guarantees: depending on how they are tuned, some of them may drive the system to an equilibrium, while others could produce cyclic, chaotic, or otherwise divergent trajectories. To account for this, we propose in 23 a range of noregret policies based on optimistic mirror descent, with the following desirable properties: i) they do not require any prior tuning or knowledge of the game; ii) they all achieve $O\left(\sqrt{T}\right)$ regret against arbitrary, adversarial opponents; and iii) they converge to the best response against convergent opponents. Also, if employed by all players, then iv) they guarantee O(1) social regret; while v) the induced sequence of play converges to Nash equilibrium with O(1) individual regret in all variationally stable games (a class of games that includes all monotone and convexconcave zerosum games).
Exploiting past information is thus essential. In 8, we study the dynamics of price discovery in decentralized twosided markets. We show that there exist memoryless dynamics that converge to the core of the underlying assignment game in which agents' actions depend only on their current payoff. However, we show that for any such dynamic the convergence time can grow exponentially in relation to the population size. We present a natural dynamic in which a player's reservation value provides a summary of his past information and show that this dynamic converges to the core in polynomial time in homogeneous markets.
8.7 Learning in Games
Participants: Kimon Antonakopoulos, Yu Guan Hsieh, Panayotis Mertikopoulos, Bary Pradelski, Patrick Loiseau.
Learning in Games is considerably more difficult than in classical minimization games as the resulting equilibria may be attractive or not and the dynamic often exhibit cyclic behaviors.
In this context, we examine in 19 the Nash equilibrium convergence properties of noregret learning in general Nplayer games. For concreteness, we focus on the archetypal "follow the regularized leader" (FTRL) family of algorithms, and we consider the full spectrum of uncertainty that the players may encounterfrom noisy, oraclebased feedback, to bandit, payoffbased information. In this general context, we establish a comprehensive equivalence between the stability of a Nash equilibrium and its support: a Nash equilibrium is stable and attracting with arbitrarily high probability if and only if it is strict (i.e., each equilibrium strategy has a unique best response). This equivalence extends existing continuoustime versions of the "folk theorem" of evolutionary game theory to a bona fide algorithmic learning setting, and it provides a clear refinement criterion for the prediction of the daytoday behavior of noregret learning in games.
We study convergence rate of a wide range of regularized methods for learning in games in 20. To that end, we propose a unified algorithmic template that we call "follow the generalized leader" (FTGL), and which includes as special cases the canonical "follow the regularized leader" algorithm, its optimistic variants, extragradient schemes, and many others. The proposed framework is also sufficiently flexible to account for several different feedback models – from full information to bandit feedback. In this general setting, we show that FTGL algorithms converge locally to strict Nash equilibria at a rate which does not depend on the level of uncertainty faced by the players, but only on the geometry of the regularizer near the equilibrium. In particular, we show that algorithms based on entropic regularizationlike the exponential weights algorithmenjoy a linear convergence rate, while Euclidean projection methods converge to equilibrium in a finite number of iterations, even with bandit feedback.
In 41, we examine the longrun behavior of a wide range of dynamics for learning in nonatomic games with finite action spaces and population games, in both discrete and continuous time. The class of dynamics under consideration includes fictitious play and its regularized variants, the best reply dynamics (again, possibly regularized), as well as the dynamics of dual averaging / "follow the regularized leader" (which themselves include as special cases the replicator dynamics and Friedman's projection dynamics). Our analysis concerns both the actual trajectory of play and its timeaverage, and we cover potential and monotone games, as well as games with an evolutionarily stable state (global or otherwise). Nonatomic games with continuous action spaces will be treated in detail in a second part.
Finally, we study the limits of minmax optimization algorithms in 25. Compared to minimization problems, the minmax landscape in machine learning applications is considerably more convoluted because of the existence of cycles and similar phenomena. Such oscillatory behaviors are wellunderstood in the convexconcave regime, and many algorithms are known to overcome them. In this paper, we go beyond the convexconcave setting and we characterize the convergence properties of a wide class of zeroth, first, and (scalable) secondorder methods in nonconvex/nonconcave problems. In particular, we show that these stateoftheart minmax optimization algorithms may converge with arbitrarily high probability to attractors that are in no way minmax optimal or even stationary. Spurious convergence phenomena of this type can arise even in twodimensional problems, a fact which corroborates the empirical evidence surrounding the formidable difficulty of training GANs.
8.8 Bandits
Participants: Yan Chen, Bruno Donassolo, Kimang Khun, Nicolas Gast, Bruno Gaujal, Arnaud Legrand, Panayotis Mertikopoulos.
The Multiarmed Stochastic Bandit framework is a classic reinforcement learning problem to study the exploration exploitation tradeoff dilemma and for which several optimal algorithms like UCB 3 and Thompson sampling4, whose optimality has only recently been proved by Kaufmann et al.5, have been proposed. Although the first strategy is an optimistic strategy which systematically chooses the "most promising" arm, the second ones build on a Bayesian perspective and samples the posterior to decide which arm to select. The Markovian Bandit allows to model situations where the reward distribution is modeled as a Markov chain and may thus exhibit temporal changes. A key challenge in this context is the curse of dimensionality, which basically says that the state size of the Markov process is exponential in the number of the system components so that the complexity of computing an optimal policy and its value are exponential.
In 39, we study learning algorithms for the classical restful Markovian bandit (in which the state of each arm evolves only when it is chosen) problem with discount and compare posterior sampling strategies with optimistic strategies in terms of scalability. We explain how to adapt PSRL and UCRL2 to exploit the problem structure (MBPSRL and MBUCRL2). While the regret bound and runtime of vanilla implementations of PSRL and UCRL2 are exponential in the number of bandits, we show that the episodic regret of MBPSRL and MBUCRL2 is $O\left(S\sqrt{nK}\right)$, where $K$ is the number of episodes, $n$ is the number of bandits, and $S$ is the number of states of each bandit. Up to a factor $\sqrt{S}$, this matches the lower bound of $\Omega \left(\sqrt{SnK}\right)$ that we also derive in the paper. MBPSRL is also computationally efficient: its runtime is linear in the number of bandits. We further show that this linear runtime cannot be achieved by adapting classical nonBayesian algorithms such as UCRL2 or UCBVI to Markovian bandit problems. Finally, we perform numerical experiments that confirm that MBPSRL outperforms other existing algorithms in practice, both in terms of regret and of computation time.
In 40, we further develop complexity results for finite horizon restless bandits (in which the state of each arm evolves according to a Markov process independently of the learner's actions). Most restless Markovian bandits problems in infinite horizon can be solved quasioptimally: the famous Whittle index policy is known to become asymptotically optimal exponentially fast as the number of arms grows, at least under certain conditions (including having a socalled indexable problem). For restless Markovian bandits problems in finite horizons no such optimal policy is known. In this paper, we define a new policy, based on a linear program relaxation of the finite horizon problem (called the LPfilling policy), that is asymptotically optimal under no condition. Furthermore we show that for regular problems (defined in the paper) the LPfilling policy becomes an index policy (called the LPregular policy) and becomes optimal exponentially fast in the number of arms. We also introduce the LPupdate policy that significantly improves the performance compared to the LPfilling policy for large time horizons. We provide numerical studies that show the prevalence of our LPpolicies over previous solutions.
Finally, in 4, we evaluate the relevance of banditlike strategies for the Fog computing context and explore the informationcoordination tradeoff. Fog computing emerges as a potential solution to handle the growth of traffic and processing demands, providing nearby resources to run IoT applications. In this paper, we consider the reconfiguration problem, i.e., how to dynamically adapt the placement of IoT applications running in the Fog, depending on application needs and evolution of resource usage. We propose and evaluate a series of reconfiguration algorithms, based on both online scheduling (dynamic packing) and online learning (bandit) approaches. Through an extensive set of experiments in a realistic testbed built on Grid5000 and FITIoT lab, we demonstrate that the performance strongly and mainly depends on the quality and availability of information from both Fog infrastructure and IoT applications. We show that a reactive and greedy strategy can overcome the performance of stateoftheart online learning algorithms, as long as the strategy has access to a little extra information.
8.9 Fairness and equity in digital (recommendation, advertising, persistant storage) systems
Participants: Dong Quan Vu, Vitalii Emelianov, Nicolas Gast, Patrick Loiseau, Benjamin Roussillon.
The general deployment of machinelearning systems in many domains ranging from security to recommendation and advertising to guide strategic decisions leads to an interesting line of research from a game theory perspective.
A first line of work in this context is related to fairness and adversarial classification. Discrimination in selection problems such as hiring or college admission is often explained by implicit bias from the decision maker against disadvantaged demographic groups. In 5, we consider a model where the decision maker receives a noisy estimate of each candidate's quality, whose variance depends on the candidate's groupwe argue that such differential variance is a key feature of many selection problems. We analyze two notable settings: in the first, the noise variances are unknown to the decision maker who simply picks the candidates with the highest estimated quality independently of their group; in the second, the variances are known and the decision maker picks candidates having the highest expected quality given the noisy estimate. We show that both baseline decision makers yield discrimination, although in opposite directions: the first leads to underrepresentation of the lowvariance group while the second leads to underrepresentation of the highvariance group. We study the effect on the selection utility of imposing a fairness mechanism that we term the $$\gamma $$rule (it is an extension of the classical fourfifths rule and it also includes demographic parity). In the first setting (with unknown variances), we prove that under mild conditions, imposing the $$\gamma $$rule increases the selection utilityhere there is no tradeoff between fairness and utility. In the second setting (with known variances), imposing the $$\gamma $$rule decreases the utility but we prove a bound on the utility loss due to the fairness mechanism.
We also consider classification in adversarial context. In 31, we consider the problem of finding optimal classifiers in an adversarial setting where the class1 data is generated by an attacker whose objective is not known to the defender – an aspect that is key to realistic applications but has so far been overlooked in the literature. To model this situation, we propose a Bayesian game framework where the defender chooses a classifier with no a priori restriction on the set of possible classifiers. The key difficulty in the proposed framework is that the set of possible classifiers is exponential in the set of possible data, which is itself exponential in the number of features used for classification. To counter this, we first show that Bayesian Nash equilibria can be characterized completely via functional threshold classifiers with a small number of parameters. We then show that this lowdimensional characterization enables us to develop a training method to compute provably approximately optimal classifiers in a scalable manner; and to develop a learning algorithm for the online setting with low regret (both independent of the dimension of the set of possible data). We illustrate our results through simulations.
The Colonel Blotto game is a wellknown resource allocation games introduced by Borel (1921) that finds application in many domains like politics (where political parties distribute their budgets to compete over voters), cybersecurity (where effort is distributed to attack/defend targets), online advertising (where marketing campaigns allocate the time to broadcast ads to attract web users), or telecommunication (where network service providers distribute and lease their spectrum to the users). In 32, we introduce the Colonel Blotto game with favoritism, an extension where the winnerdetermination rule is generalized to include preallocations and asymmetry of the players' resources effectiveness on each battlefield. Such favoritism is found in many classical applications of the Colonel Blotto game. We focus on the Nash equilibrium. First, we consider the closely related model of allpay auctions with favoritism and completely characterize its equilibrium. Based on this result, we prove the existence of a set of optimal univariate distributionswhich serve as candidate marginals for an equilibriumof the Colonel Blotto game with favoritism and show an explicit construction thereof. In several particular cases, this directly leads to an equilibrium of the Colonel Blotto game with favoritism. In other cases, we use these optimal univariate distributions to derive an approximate equilibrium with wellcontrolled approximation error. Finally, we propose an algorithmbased on the notion of winding number in parametric curvesto efficiently compute an approximation of the proposed optimal univariate distributions with arbitrarily small error.
Finally, we propose in 28, a gametheoretic analysis of the transaction ordering protocol in the Bitcoin blockchain. Most public blockchain protocols, including the popular Bitcoin and Ethereum blockchains, do not formally specify the order in which miners should select transactions from the pool of pending (or uncommitted) transactions for inclusion in the blockchain. Over the years, informal conventions or "norms" for transaction ordering have, however, emerged via the use of shared software by miners, e.g., the GetBlockTemplate (GBT) mining protocol in Bitcoin Core. Today, a widely held view is that Bitcoin miners prioritize transactions based on their offered "transaction feeperbyte. " Bitcoin users are, consequently, encouraged to increase the fees to accelerate the commitment of their transactions, particularly during periods of congestion. In this paper, we audit the Bitcoin blockchain and present statistically significant evidence of mining pools deviating from the norms to accelerate the commitment of transactions for which they have (i) a selfish or vested interest, or (ii) received darkfee payments via opaque (nonpublic) sidechannels. As blockchains are increasingly being used as a recordkeeping substrate for a variety of decentralized (financial technology) systems, our findings call for an urgent discussion on defining neutrality norms that miners must adhere to when ordering transactions in the chains.
8.10 Policy responses to Covid19
Participants: Nicolas Gast, Bruno Gaujal, Bary Pradelski.
The Covid19 pandemic has deeply impacted our lives and caused more than 5.49 million deaths worldwide, making it one of the deadliest pandemic in history. Several policies have been proposed to respond this illness and mitigate both its spread and its impact on both populations' health and economy. We have been studying and supporting some of policies through our expertise in large system analysis (game theory, mean field, etc.)
Bary Pradelski has been among the first researchers to actively promote Green zoning which has emerged as a widely used policy response to tackle the Covid19 pandemic 10. ‘Green zones’ – areas where the virus is under control based on a uniform set of conditions – can progressively return to normal economic and social activity levels, and mobility between them is permitted. By contrast, stricter public health measures are in place in ‘red zones’, and mobility between red and green zones is restricted. France and Spain were among the first countries to introduce green zoning in April 2020. Subsequently, more and more countries followed suit and the European Commission advocated for the implementation of a European green zoning strategy, which has been supported by the EU member states. While there remain coordination problems, green zoning has proven to be an effective strategy for containing the spread of the virus and limiting its negative economic and social impact. This strategy should provide important lessons and prove useful in future outbreaks. Research in epidemiology indicates that thoroughly implemented and operationalised green zoning can prevent the spread of a transmittable disease that is poorly understood, highly virulent, and potentially highly lethal. Finally, there is strong evidence that green zoning can reduce economic and societal damage as it avoids worstinclass measures.
Unfortunately, locking down entire regions is not satisfactory and has dramatic consequences on health, the economy, and civil liberties, and several countries have responded in very different ways. Some countries have consistently aimed for elimination – i.e., maximum action to control SARSCoV2 and stop community transmission as quickly as possible – while others have opted for mitigation – i.e., action increased in a stepwise, targeted way to reduce cases so as not to overwhelm healthcare systems. In 9, we show that the former ones have generally fared much better than the latter ones by comparing deaths, gross domestic product (GDP) growth, and strictness of lockdown measures during the first 12 months of the pandemic. Furthermore, the mitigation has favored the proliferation of new SARSCoV2 variants and countries that opt to live with the virus will likely pose a threat to other countries, notably those that have less access to COVID19 vaccines. Although many scientists have called for a coordinated international strategy to eliminate SARSCoV2, it has unfortunately not been heard yet.
Finally, we analyze in 18 a virus propagation dynamics in a large population of agents (or nodes) with three possible states (Susceptible, Infected, Recovered) where agents may choose to vaccinate. We show that this system admits a unique symmetric equilibrium when the number of agents goes to infinity. We also show that the vaccination strategy that minimizes the social cost has the same threshold structure as the mean field equilibrium, but with a shorter threshold. This implies that, to encourage optimal vaccination behavior, vaccination should always be subsidized.
9 Bilateral contracts and grants with industry
Participants: Till Kletti, Patrick Loiseau.
Patrick Loiseau has a Cifre contract with Naver labs (20202023) on "Fairness in multistakeholder recommendation platforms”, which supports the PhD student Till Kletti.
10 Partnerships and cooperations
Participants: Nicolas Gast, Guillaume Huard, Patrick Loiseau, Panayotis Mertikopoulos, Bary Pradelski, Benjamin Roussillon.
10.1 International initiatives
10.1.1 Associate Teams in the framework of an Inria International Lab or in the framework of an Inria International Program
ReDaS

Title:
Reproducible Data Science

Duration:
2019 – 2021

Coordinator:
Guillaume Huard and Lucas Mello Schnorr

Partners:
Universidade Federal do Rio Grande do Sul

Inria contact:
Guillaume Huard

Summary:
The main scientific context of this project is to develop novel analysis techniques and workflow methodologies to support reproducible data science. We focus our efforts along three axes:
 Analysis Techniques: large volumes of data are hard to summarize using simple statistics that hides important behavior in the data. Therefore, raw information visualization plays a key role to explore such data, in particular when curating data and trying to develop intuition about the mathematical models underlying data. Yet, such visualizations require data aggregation, which may lead to significant information loss. It is thus essential to investigate adaptive data aggregation schemes that enable the reduction of the data while controlling the information loss.
 Workflow Methodologies: the analysis process often involves a mix of tools to produce the end result. The data has to be filtered before it can be passed to some standard statistical tool to, eventually, produce some projection of the transformed data that can be visualized and studied by the analyst. Furthermore, the process is interactive: when the analyst is unsatisfied with the end result, a part of the analysis has to be changed to produce a new visualization. These adaptations of the whole analysis typically start from intermediate data and only a part of the analysis has to be rerun. The issue comes with the increasing size of these analysis, the disparity of the analysis tools and the large space of analysis parameters.

Evaluation: In the previous work packages we will propose both a theoretical and practical methodology whose relevance should be evaluated with real case studies. We will build our evaluation on well identified and quite different datasets originating from the following three areas, on which we already have some past experience:

Performance analysis of HPC applicationsThese applications and their underlying runtimes tend to be increasingly complex and dynamic. As a consequence, their execution traces become too large and impossible to analyze with classical tools.

Longterm phenology behavior analysis and correlation with climate changeThe phenology is the study of plant grow through the use of digital cameras attached to towers installed in the middle of the natural environments. These cameras take photos every a certain number of minutes and enable the researcher to verify how certain species grow, including their relation with the climate.

General public datasets from governement transparency reportsAll public Brazilian institutions are obliged by law to provide datasets about any publiclyfinanced data measurements. The city of Porto Alegre has longterm weather datasets that contain temperature, pressure and other indicators from different parts of the city. The goal in this case study is very exploratory, for example to envision a way to represent such data in a geographical manner to verify if certain parts of the city may suffer from flash flood more than others.

Performance analysis of HPC applications
10.2 National initiatives
ANR

ANR ORACLESS (JCJC 20162021)$\u2606$
Online Resource Allocation, unprediCtable wireLESs Systems
[207K€] ORACLESS is an ANR starting grant (JCJC) coordinated by Panayotis Mertikopoulos. The goal of the project is to develop highly adaptive resource allocation methods for wireless communication networks that are provably capable of adapting to unpredictable changes in the network. In particular, the project will focus on the application of online optimization and online learning methodologies to multiantenna systems and cognitive radio networks.

ANR ALIAS (PRCI 20202021)$\u2606$
Adaptive Learning for Interactive Agents and Systems
[284K€] Partners: Singapore University of Technology and Design (SUTD).
ALIAS is a bilateral PRCI (collaboration internationale) project joint with Singapore University of Technology and Design (SUTD), coordinated by Bary Pradelski (PI) and involving P. Mertikopoulos and P. Loiseau. The Singapore team consists of G. Piliouras and G. Panageas. The goal of the project is to provide a unified answer to the question of stability in multiagent systems: for systems that can be controlled (such as programmable machine learning models), prescriptive learning algorithms can steer the system towards an optimum configuration; for systems that cannot (e.g., online assignment markets), a predictive learning analysis can determine whether stability can arise in the long run. We aim at identifying the fundamental limits of learning in multiagent systems and design novel, robust algorithms that achieve convergence in cases where conventional online learning methods fail.

ANR REFINO (JCJC 20202024)$\u2606$
Refined Mean Field Optimization
[250K€] REFINO is an ANR starting grant (JCJC) coordinated by Nicolas Gast. The main objective on this project is to provide an innovative framework for optimal control of stochastic distributed agents. Restless bandit allocation is one particular example where the control that can be sent to each arm is restricted to an on/off signal. The originality of this framework is the use refined mean field approximation to develop control heuristics that are asymptotically optimal as the number of arms goes to infinity and that also have a better performance than existing heuristics for a moderate number of arms. As an example, we will use this framework in the context of smart grids, to develop control policies for distributed electric appliances.

ANR FAIRPLAY (JCJC 20212025)$\u2606$
Fair algorithms via game theory and sequential learning
[245K€] FAIRPLAY is an ANR starting grant (JCJC) coordinated by Patrick Loiseau. Machine learning algorithms are increasingly used to optimize decision making in various areas, but this can result in unacceptable discrimination. The main objective of this project is to propose an innovative framework for the development of learning algorithms that respect fairness constraints. While the literature mostly focuses on idealized settings, the originality of this framework and central focus of this project is the use of game theory and sequential learning methods to account for constraints that appear in practical applications: strategic and decentralized aspects of the decisions and the data provided and absence of knowledge of certain parameters key to the fairness definition.
DGA Grants
Patrick Loiseau and Panayotis Mertikopoulos have a grant from DGA (20182021) that complements the funding of PhD student (Benjamin Roussillon) to work on game theoretic models for adversarial classification.
IRS/UGA
Projet DISCMAN (projet IRS de l'UGA). DISCMAN (Distributed Control for MultiAgent systems and Networks) is a joint IRS project funded by IDEX Université GrenobleAlpes. Its main objectives is to develop distributed equilibrium convergence algorithms for largescale control and optimization problems, both offline and online. It is being coordinated by P. Mertikopoulos (POLARIS), and it involves a joint team of researchers from the LIG and LJK laboratories in Grenoble.
11 Dissemination
Participants: Jonatha Anselmi, Romain Couillet, Vincent Danjean, Nicolas Gast, Bruno Gaujal, Guillaume Huard, Arnaud Legrand, Patrick Loiseau, Panayotis Mertikopoulos, Bary Pradelski.
11.1 Promoting scientific activities
11.1.1 Scientific events: organisation
General chair, scientific chair
 P. Loiseau has been chair of the steering committee of NetEcon;
11.1.2 Scientific events: selection
Chair of conference program committees
 P. Mertikopoulos has been a TPC cochair for NetGCoOp 2020 (online, postponed from 2020), area chair for NeurIPS 2021, and area chair for ICLR 2021
Member of the conference program committees
 P. Loiseau has been a PC member of AAAI 2021, ECMLPKDD 2021 (Area Chair), FAccT 2021 (Area Chair), and NetEcon;
 J. Anselmi has been a PC member of IFIP Performance 2021 and IEEE MASCOTS 2021
 N. Gast has been a PC member of Sigmetrics 2021 and NeurIPS 2021.
 B. Pradelski has been a PC member of FAT* 2021.
Reviewer
 B. Gaujal has been a reviewer for ACM Sigmetrics
11.1.3 Journal
Member of the editorial boards
 N. Gast is associate editor for Performance Evaluation and Stochastic Models.
 R. Couillet is associate editor for Random Matrix Theory and Applications.
 P. Mertikopoulos is an associate editor for Operations Research Letters, RAIRO Operations Research, EURO Journal on Computational Optimization, Journal on Dynamics and Games, Methodology and Computing in Applied Probability, Reviewer for:, Games and Economic Behavior, Journal of Economic Theory, Journal of Optimization Theory and Applications, Mathematics of Operations Research, Mathematical Programming, Operations Research, SIAM Journal on Control and Optimization, and SIAM Journal on Optimization
Reviewer  reviewing activities
 P. Loiseau has been a reviewer for Games and Economics Behavior
 B. Gaujal has been a reviewer for CHAOS and Games and Economic Behavior.
 B. Pradelski has been a reviewer for Games and Economic Behavior, Operations Research, and International Journal of Game Theory
11.1.4 Invited talks
 B. Gaujal has been invited to give a talk on Discrete Mean Field Games to the monthly seminar of the Gipsa Lab, Grenoble, in October 2021;
 J. Anselmi has been invited to give a talk on Stability and Optimization of Speculative Queueing Networks at the 2021 INFORMS Annual Meeting;
 R. Couillet has been invited several time to expose his work on sustainable AI and the anthropocene (ENS Paris, Ecole Polytechnique, TU Berlin, etc.).
 B. Pradelsky has been invited to present his work on The effect of COVID certificates on vaccine uptake, health outcomes, and the economy to the Brusselsbased economic think tank Bruegel.
 P. Mertikopoulos has been invited to present his work on:
 Adaptive Routing in Largescale Networks: Optimality Under Uncertainty at NYU Operations Management Series
 Online learning in games at NTUA (Computation and Reasoning Laboratory)
 Generalized RobbinsMonro algorithms for minmin and minmax optimization at RWTH Aachen (Mathematics and Information Processing Seminar)
 Online optimization: A unified view through the lens of stochastic approximation at Télécom ParisTech (Signal, Statistics & Learning Seminar)
 Dynamics, (minmax) optimization, and games at TSE (MADStat Seminar)
 Spurious attractors in minmax optimization at Montréal Machine Learning and Optimization Seminar
 Optimization, games, and dynamical systems at TOUTELIA 2021, Toulouse
 A. Legrand has been invited to give lectures on Open Science and Reproducible Research at:
 Laboratory Notebooks and Reproducible Research at the DKM department of the IRISA laboratory, Feb 2021.
 Reproducibility Crisis and Open Science at the UGA Reproducible Research seminar, Apr 2021.
 Obtaining Faithful/Reproducible Measurements on Modern CPUs at the Journée SIF on research reproducibility, May 2021.
 Generating a Controled Software Environment with Debian Snapshot Archive at the GUIX workhop on software environment reproducibility, May 2021.
 Reproducibility Crisis and Open Science at the reproducible research workshop of the Montpellier BioStats network
 Reproducibility Crisis and Open Science at the Sciences de l'information géographique reproductibles thematic school of the CISTCNRS.
11.1.5 Research Administration
 P. Loiseau is an expert for the FRSFNRS
 A. Legrand has participated to the Electronic Laboratory Notebook working group of the French CoSO (Comité pour la Science Ouverte), whose report has recently been produced.
 A. Legrand is a member of the Inria Grenoble COS (conseil scientifique);
 A. Legrand is a member of the CoSO UGA board (commission consultative science ouverte);
 A. Legrand is in charge of the Distributed Systems, Parallel Computing, and Networks research area theme of the LIG;
 N. Gast is coresponsible of the PhD program in Computer Science at the University GrenobleAlpes (vice director of ED MSTII).
11.2 Teaching  Supervision  Juries
 B. Gaujal has been a member of the jury for CR2 selection in Inria Grenoble
 A. Legrand is a member of the section 6 of the CoNRS (Comité National de la Recherche Scientifique)
 N. Gast served in the « Comité de spécialistes » (COS) for a MCF position in the GSCOP laboratory (Grenoble)
 P. Mertikopoulos served in the « Comité de spécialistes » (COS) for a MCF position in the Université Gustave Eiffel.
 A. Legrand served in the « Comité de spécialistes » (COS) for a Professor position in the ENS Rennes.
 A. Legrand was a reviewer for the PhD thesis of Mrs Yiqin Gao, from ENS Lyon: Scheduling independent tasks under budget and time constraints
 P. Mertikopoulos was a member of the PhD thesis committee of Mr. Yassine Laguel from UGA: Optimisation convexe pour l’apprentissage robuste au risque
 A. Legrand is a member of the midterm PhD committee of Adeyemi Adetula (UGA)
 P. Loiseau is a member of the midterm PhD committee of O. Boufous (U. Avignon) and C. Pinzon (Ecole Polytechnique)
 B. Gaujal is a member of the midterm PhD committee of Michel Davydov (ENS Paris)
11.2.1 Teaching
 J. Anselmi teaches the Probability and Simulation and the Performance Evaluation lectures in M1, Polytech Grenoble.
 P. Loiseau teaches the M1 course at Ecole Polytechnique on Advanced Machine Learning and Autonomous Agents
 A. Legrand and J.M. Vincent teach the transversal Scientific Methodology and Empirical Evaluation lecture (36h) at the M2 MOSIG.
 B. Gaujal teaches the M2 course on Optimization under uncertainties in M2 ORCO Grenoble
 N. Gast is responsible of the course Reinforcement Learning in Master MOSIG/MSIAM (Grenoble) and of the course « Introduction to machine learning » (License 3, Grenoble).
 G. Huard is responsible of the courses UNIX & C programming in the L1 and L3 INFO, of Object oriented and eventdriven programming in the L3 INFO, and of the Objet oriented design in M1 INFO.
 During the COVID crisis, teaching as been particularly difficult and has required major involvements and adaptations of teachers. G. Huard has implemented the following developments related to teaching activities:
 Moodle VPL backend & engine for local execution
 VSCode extensions to use VPLs and help with C programming (here and here)
 Several VPL activities for the course in L1 INFO on Moodle
 V. Danjean teaches the Operating Systems, Programming Languages, Algorithms, Computer Science and Mediation lectures in L3, M1 and Polytech Grenoble.
 V. Danjean organized with J.M. Vincent the end of the DIUEIL that have been setup for training high school professors to teach computer science.
 R. Couillet is the initiator of a new lecture on the introduction to artificial intelligence in the L1 INFO.
 The 3rd edition of the MOOC of A. Legrand, K. Hinsen and C. Pouzat on Reproducible research: Methodological principles for a transparent science is still running. Over the 3 editions (Oct.Dec. 2018, Apr.June 2019, March 2020  end of 2022), about 17,800 persons have followed this MOOC and 1620 certificates of achievement have been delivered. 54% of participants are PhD students and 12% are undergraduates.
 A. Legrand has organized with F. Theoleyre, B. Dnnassolo, M. Simonin, and G. Schreiner the 16th edition of the RSD GDR research school on Reproducibility and experimental research in networks and systems. This school has attrated 40 PhD students and has offered them to experiment with both the Grid5000 and FITIoTLab platforms throughout the whole week using reproducible research technologies (Jupyter notebooks, docker containers, git, the EnOSLib experiment engine, R for data analysis and experiment design, etc.). See here and here for more details.
11.3 Popularization
 V. Danjean organized a Linux Install Party for all the students of INFO and IESE3 department of Polytech'Grenoble
 R. Couillet has been interviewed by France Bleu Isère in the Retour sur Terre show (Dec. 9th 2021)
The efforts of B. Pradelski on COVID policy has received lots of media coverage in Le Monde and other major newspapers. See for example:
 Le Monde: Couverture vaccinale: nombre de décès et PIB, le très fort impact du passe sanitaire
 Les Echos: CoViD: le passe sanitaire a sauvé 4000 vies en France entre mijuillet et fin 2021
 Financial Times: Covid passes boosted economies and vaccine uptake, study shows
 The Lancet article SARSCoV2 elimination, not mitigation, creates best outcomes for health, the economy, and civil liberties9 has been covered in the New York Times, Financial Times, Daily Mail, Süddeutsche Zeitung, Le Monde, Libération, Le Temps, Euronews, Le Devoir, The Hill, 20 minutos, Die Welt, The Guardian (five times), New Scientist, The Atlantic, Exame, L’Express, Die Zeit, Science, Politico
 Several opinion articles have also been published in media:
 ‘Covid19 : « Le passe sanitaire doit servir à accélérer les doses de rappel »’ with Miquel OliuBarton, Le Monde (24 November 2021).
 ‘Covid19 : le faux dilemme entre santé, économie et libertés’ with Philippe Aghion, Patrick Artus, and Miquel OliuBarton, Commentaire (June 2021).
 ‘Le recours temporaire à un passe sanitaire est nécessaire si nous voulons une sortie de crise durable’ with Philippe Aghion, Philippe Martin, and Miquel OliuBarton, Le Monde (2 June 2021).
 ‘Covid19 : « Nous avons besoin d’un “passe sanitaire” fiable, temporaire et accessible pour tout le monde »’ with Anne Bucher and Miquel OliuBarton, Le Monde (22 March 2021).
 ‘Aiming for zero Covid19: Europe needs to take action’ with a group of international scientists, published by Bruegel, de Volkskrant, El Pais, la Repubblica, Le Monde, Rzeczpospolita, Süddeutsche Zeitung (15 February 2021).
12 Scientific production
12.1 Publications of the year
International journals
 1 articleStability and Optimization of Speculative Queueing Networks.IEEE/ACM Transactions on Networking2021, 112
 2 articleDispatching to parallel servers: Solutions of Poisson's equation for firstpolicy improvement.Queueing Systems993October 2021, 199–230
 3 articleMinibatch forwardbackwardforward methods for solving stochastic variational inequalities.Stochastic Systems112June 2021, 112139
 4 articleOnline Reconfiguration of IoT Applications in the Fog: The InformationCoordination Tradeoff.IEEE Transactions on Parallel and Distributed Systems3352022, 11561172
 5 articleOn fair selection in the presence of implicit and differential variance.Artificial Intelligence302October 2021, 120
 6 articleAnalysis of Work Stealing with latency.Journal of Parallel and Distributed Computing153July 2021, 119129
 7 articleA PseudoLinear Time Algorithm for the Optimal Discrete Speed Minimizing Energy Consumption.Discrete Event Dynamic Systems2021
 8 articleThe importance of memory for price discovery in decentralized markets.Games and Economic Behavior125January 2021, 6278
 9 articleSARSCoV2 elimination, not mitigation, creates best outcomes for health, the economy, and civil liberties.The Lancet39710291June 2021, 22342236
 10 articleGreen zoning: An effective policy tool to tackle the Covid19 pandemic.Health Policy1258August 2021, 981986
 11 articleDistributed stochastic optimization with large delays.Mathematics of Operations Research2021, 141
 12 articleRobust power management via learning and game design.Operations Research691January 2021, 331345
International peerreviewed conferences
 13 inproceedingsrmftool  A library to Compute (Refined) Mean Field Approximation(s).TOSME 2021Online conference, FranceNovember 2021
 14 inproceedingsAdaptive extragradient methods for minmax optimization and games.ICLR 2021  9th International Conference on Learning RepresentationsVirtual, Unknown RegionMay 2021, 128
 15 inproceedingsAdaptive firstorder methods revisited: Convex optimization without Lipschitz requirements.NeurIPS 2021  35th International Conference on Neural Information Processing SystemsVirtual, Unknown Region2021
 16 inproceedingsSifting through the noise: Universal firstorder methods for stochastic variational inequalities.NeurIPS 2021  35th International Conference on Neural Information Processing SystemsVirtual, Unknown RegionDecember 2021, 139
 17 inproceedingsThe lastiterate convergence rate of optimistic mirror descent in stochastic variational inequalities.COLT 2021  34th Annual Conference on Learning TheoryBoulder, United StatesAugust 2021, 132
 18 inproceedingsVaccination in a Large Population: Mean Field Equilibrium versus Social Optimum.NETGCOOP 2020  10th International Conference on NETwork Games, COntrol and OPtimizationCargèse, FranceSeptember 2021, 19
 19 inproceedingsSurvival of the strictest: Stable and unstable equilibria under regularized learning with partial information.COLT 2021  34th Annual Conference on Learning TheoryBoulder, United StatesAugust 2021, 130
 20 inproceedingsThe convergence rate of regularized learning in games: From bandits and uncertainty to optimism and beyond.NeurIPS 2021  35th International Conference on Neural Information Processing SystemsVirtual, Unknown RegionDecember 2021, 128
 21 inproceedingsRegret minimization in stochastic nonconvex learning via a proximalgradient approach.ICML 2021  38th International Conference on Machine LearningVienna, AustriaJuly 2021
 22 inproceedingsZerothorder nonconvex learning via hierarchical dual averaging.ICML 2021  38th International Conference on Machine LearningVienna, AustriaJuly 2021, 134
 23 inproceedingsAdaptive learning in continuous games: Optimal regret bounds and convergence to Nash equilibrium.COLT 2021  the 34th Annual Conference on Learning TheoryBoulder, United StatesAugust 2021, 134
 24 inproceedingsOptimization in open networks via dual averaging.CDC 2021  60th IEEE Annual Conference on Decision and ControlAustin, United StatesIEEEDecember 2021, 17
 25 inproceedingsThe limits of minmax optimization algorithms: Convergence to spurious noncritical sets.ICML 2021  38th International Conference on Machine LearningVienna, AustriaJuly 2021
 26 inproceedingsIntroducing the Expohedron for Efficient Paretooptimal FairnessUtility Amortizations in Repeated Rankings.WSDM 2022  15th ACM International Conference on Web Search and Data MiningPhoenix (virtual), United StatesACMFebruary 2022, 110
 27 inproceedingsEquilibrium tracking and convergence in dynamic games.CDC 2021  60th IEEE Annual Conference on Decision and ControlAustin, United StatesDecember 2021, 18
 28 inproceedingsSelfish & Opaque Transaction Ordering in the Bitcoin Blockchain: The Case for Chain Neutrality.IMC 2021  ACM Internet Measurement ConferenceVirtual Event, FranceNovember 2021, 116
 29 inproceedingsExploiting system level heterogeneity to improve the performance of a GeoStatistics multiphase taskbased application.ICPP 2021  50th International Conference on Parallel ProcessingLemont, United StatesAugust 2021, 110
 30 inproceedingsFast routing under uncertainty: Adaptive learning in congestion games with exponential weights.NeurIPS 2021  35th International Conference on Neural Information Processing SystemsVirtual, Unknown RegionDecember 2021, 136
 31 inproceedingsScalable Optimal Classifiers for Adversarial Settings under Uncertainty.GameSec 2021  12th Conference on Decision and Game Theory for SecurityPrague, Czech Republic2021, 120
 32 inproceedingsColonel Blotto Games with Favoritism: Competitions with Preallocations and Asymmetric Effectiveness.Proceedings of the 22nd ACM Conference on Economics and Computation (ACM EC '21)Budapest, HungaryJuly 2021, 862863
Doctoral dissertations and habilitation theses
 33 thesisHigh Performance Computing : towards better Performance Predictions and Experiments.Université Grenoble Alpes [2020....]June 2021
 34 thesisToward transparent and parsimonious methods for automatic performance tuning.UGA (Université Grenoble Alpes); USP (Universidade de São Paulo)July 2021
 35 thesisLearning in the Presence of Strategic Data Sources: Models and Solutions.Université Grenoble AlpesSeptember 2021
Reports & preprints
 36 miscOptimal Speed Profile of a DVFS Processor under Soft Deadlines.October 2021
 37 miscSimulationbased Optimization and Sensibility Analysis of MPI Applications: Variability Matters.January 2022
 38 miscMultiagent online learning in timevarying games.2021
 39 misc Reinforcement Learning for Markovian Bandits: Is Posterior Sampling more Scalable than Optimism? June 2021
 40 misc(Close to) Optimal Policies for Finite Horizon Restless Bandits.June 2021
 41 miscLearning in nonatomic games, Part I: Finite action spaces and population games.September 2021
 42 miscMultiagent online optimization with delays: Asynchronicity, adaptivity, and optimism.2021
 43 miscPerformance Analysis of Irregular TaskBased Applications on Hybrid Platforms: Structure Matters.July 2021
12.2 Cited publications
 44 inproceedingsMeasuring the Facebook Advertising Ecosystem.NDSS 2019  Proceedings of the Network and Distributed System Security SymposiumSan Diego, United StatesFebruary 2019, 115
 45 inproceedingsInvestigating Ad Transparency Mechanisms in Social Media: A Case Study of Facebook's Explanations.NDSS 2018  Network and Distributed System Security SymposiumSan Diego, United StatesFebruary 2018, 115
 46 articleCombining SizeBased Load Balancing with RoundRobin for Scalable Low Latency.IEEE Transactions on Parallel and Distributed Systems2019, 13
 47 articleAsymptotically Optimal SizeInterval Task Assignments.IEEE Transactions on Parallel and Distributed Systems30112019, 24222433
 48 articlePowerofdChoices with Memory: Fluid Limit and Optimality.Mathematics of Operations Research4532020, 862888
 49 inproceedingsDimemas: Predicting MPI Applications Behaviour in Grid Environments.Proc. of the Workshop on Grid Applications and Programming Tools2003
 50 conferencexSim: The ExtremeScale Simulator.HPCSIstanbul, Turkey2011
 51 inproceedingsAutotuning under Tight Budget Constraints: A Transparent Design of Experiments Approach.CCGrid 2019  International Symposium in Cluster, Cloud, and Grid ComputingLarcana, CyprusIEEEMay 2019, 110
 52 incollectionComprehensive Performance Tracking with VAMPIR 7.Tools for High Performance Computing 2009The paper details the latest improvements in the Vampir visualization tool.Springer Berlin Heidelberg2010
 53 articlePenaltyRegulated Dynamics and Robust Learning Procedures in Games.Mathematics of Operations Research4032015, 611633
 54 articlePerformance analysis methods for listbased caches with nonuniform access.IEEE/ACM Transactions on NetworkingDecember 2020, 118
 55 inproceedingsEquality of Voice: Towards Fair Representation in Crowdsourced TopK Recommendations.FAT* 2019  ACM Conference on Fairness, Accountability, and TransparencyProceedings of the ACM Conference on Fairness, Accountability, and Transparency (FAT*)Atlanta, United StatesACMJanuary 2019, 129138
 56 inproceedingsFast and Faithful Performance Prediction of MPI Applications: the HPL Case Study.2019 IEEE International Conference on Cluster Computing (CLUSTER)Albuquerque, United StatesSeptember 2019
 57 articleSimulating MPI applications: the SMPI approach.IEEE Transactions on Parallel and Distributed Systems288August 2017, 14
 58 inproceedingsLoad Aware Provisioning of IoT Services on Fog Computing Platform.IEEE International Conference on Communications (ICC)Shanghai, ChinaIEEEMay 2019
 59 inproceedings Are meanfield games the limits of finite stochastic games? The 18th Workshop on MAthematical performance Modeling and Analysis Nice, France June 2016
 60 articleDiscrete Mean Field Games: Existence of Equilibria and Convergence.Journal of Dynamics and Games632019, 119
 61 unpublishedLearning in timevarying games.October 2018, Under review in MOR
 62 inproceedingsThe Price of Local Fairness in Multistage Selection.IJCAI2019  TwentyEighth International Joint Conference on Artificial IntelligenceMacao, FranceInternational Joint Conferences on Artificial Intelligence OrganizationAugust 2019, 58365842
 63 inproceedingsOn Fair Selection in the Presence of Implicit Variance.EC 2020  TwentyFirst ACM Conference on Economics and ComputationBudapest, HungaryACMJuly 2020, 649–675
 64 inproceedingsNoregret learning and mixed Nash equilibria: They do not mix.NeurIPS 2020  34th International Conference on Neural Information Processing SystemsVancouver, CanadaDecember 2020, 124
 65 articleA Visual Performance Analysis Framework for Taskbased Parallel Applications running on Hybrid Clusters.Concurrency and Computation: Practice and Experience3018April 2018, 131
 66 articleSize Expansions of Mean Field Approximation: Transient and SteadyState Analysis.Performance Evaluation2018, 115
 67 inproceedingsExpected Values Estimated via MeanField Approximation are 1/NAccurate.ACM SIGMETRICS / International Conference on Measurement and Modeling of Computer Systems , SIGMETRICS '171ACM SIGMETRICS / International Conference on Measurement and Modeling of Computer Systems , SIGMETRICS '17UrbanaChampaign, United StatesJune 2017, 26
 68 unpublishedExponential Convergence Rate for the Asymptotic Optimality of Whittle Index Policy.December 2020,
 69 inproceedingsA Refined Mean Field Approximation.ACM SIGMETRICS 2018Irvine, United StatesJune 2018, 1
 70 articleLinear Regression from Strategic Data Sources.ACM Transactions on Economics and Computation82May 2020, 124
 71 inproceedingsA Refined Mean Field Approximation for Synchronous Population Processes.MAMA 2018Workshop on MAthematical performance Modeling and AnalysisIrvine, United StatesJune 2018, 13
 72 inproceedingsAsymptotically Exact TTLApproximations of the Cache Replacement Algorithms LRU(m) and hLRU.28th International Teletraffic Congress (ITC 28)Würzburg, GermanySeptember 2016
 73 articleTTL Approximations of the Cache Replacement Algorithms LRU(m) and hLRU.Performance EvaluationSeptember 2017
 74 inproceedingsA Linear Time Algorithm for Computing Offline Speed Schedules Minimizing Energy Consumption.MSR 2019  12ème Colloque sur la Modélisation des Systèmes RéactifsAngers, FranceNovember 2019, 114
 75 inproceedingsDiscrete and Continuous Optimal Control for Energy Minimization in RealTime Systems.EBCCSP 2020  6th International Conference on EventBased Control, Communication, and Signal ProcessingKrakow, PolandIEEESeptember 2020, 18
 76 articleDynamic Speed Scaling Minimizing Expected Energy Consumption for RealTime Tasks.Journal of SchedulingJuly 2020, 125
 77 techreportExploiting Job Variability to Minimize Energy Consumption under RealTime Constraints.RR9300Inria Grenoble RhôneAlpes, Université de Grenoble ; Université Grenoble  AlpesNovember 2019, 23
 78 articleVisualizing the performance of parallel programs.IEEE software85The paper presents Paragraph.1991
 79 inproceedingsPredicting the Energy Consumption of MPI Applications at Scale Using a Single Node.Cluster 2017IEEEHawaii, United StatesSeptember 2017
 80 inproceedingsLogGOPSim  Simulating LargeScale Applications in the LogGOPS Model.ACM Workshop on LargeScale System and Application Performance2010
 81 articleScaling applications to massively parallel machines using Projections performance analysis tool.Future Generation Comp. Syst.2232006
 82 inproceedingsUsing Simulation to Evaluate and Tune the Performance of Dynamic Load Balancing of an Overdecomposed Geophysics Application.EuroPar 2017: 23rd International European Conference on Parallel and Distributed ComputingSantiago de Compostela, SpainAugust 2017, 15
 83 articlePerformance Modeling of a Geophysics Application to Accelerate the Tuning of Overdecomposition Parameters through Simulation.Concurrency and Computation: Practice and Experience2018, 121
 84 inproceedingsASGriDS: Asynchronous SmartGrids Distributed Simulator.APPEEC 2019  11th IEEE PES AsiaPacific Power and Energy Engineering ConferenceMacao, Macau SAR ChinaIEEEDecember 2019, 15
 85 inproceedingsSelection Problems in the Presence of Implicit Bias.Proceedings of the 9th Innovations in Theoretical Computer Science Conference (ITCS)2018, 33:133:17
 86 inproceedingsAdapting Batch Scheduling to Workload Characteristics: What can we expect From Online Learning?IPDPS 2019  33rd IEEE International Parallel & Distributed Processing SymposiumRio de Janeiro, BrazilIEEEMay 2019, 686695
 87 inproceedingsCollisions groupées lors du mécanisme d'évitement de collisions de CPLG3.CoRes 2020  Rencontres Francophones sur la Conception de Protocoles, l’Évaluation de Performance et l’Expérimentation des Réseaux de CommunicationLyon, FranceSeptember 2020, 14
 88 inproceedingsOptimistic Mirror Descent in SaddlePoint Problems: Going the Extra (Gradient) Mile.ICLR 2019  7th International Conference on Learning RepresentationsNew Orleans, United StatesMay 2019, 123
 89 inproceedingsQuick or cheap? Breaking points in dynamic markets.EC 2020  21st ACM Conference on Economics and ComputationBudapest, HungaryJuly 2020, 132
 90 inproceedingsCycles in adversarial regularized learning.SODA '18  TwentyNinth Annual ACMSIAM Symposium on Discrete AlgorithmsNew Orleans, United StatesJanuary 2018, 27032717
 91 articleLearning in games via reinforcement learning and regularization.Mathematics of Operations Research414November 2016, 12971324
 92 articleRiemannian game dynamics.Journal of Economic Theory177September 2018, 315364
 93 inproceedingsForgetting the Forgotten with Lethe: Conceal Content Deletion from Persistent Observers.PETS 2019  19th Privacy Enhancing Technologies SymposiumStockholm, SwedenJuly 2019, 121
 94 articleVAMPIR: Visualization and Analysis of MPI Resources.Supercomputer1211996
 95 techreportA vaccination policy by zones.Think tank Terra NovaOctober 2020
 96 inproceedingsGreen bridges: Reconnecting Europe to avoid economic disaster.Europe in the Time of Covid192020
 97 inproceedingsPARAVER: A tool to visualise and analyze parallel code.Proceedings of Transputer and Occam Developments, WOTUG18.441995
 98 articleMarket sentiments and convergence dynamics in decentralized assignment economies.International Journal of Game Theory491March 2020, 275298
 99 techreportFocus mass testing: How to overcome low test accuracy.Esade Centre for Economic PolicyDecember 2020
 100 inproceedingsScalable performance analysis: the Pablo performance analysis environment.Scalable Parallel Libraries Conference1993
 101 inproceedingsThe eyes have it: A task by data type taxonomy for information visualizations.IEEE Symposium on Visual LanguagesIEEE1996
 102 inproceedingsPower Management and Dynamic Voltage Scaling: Myths and Facts.Proceedings of the 2005 Workshop on Power Aware Realtime ComputingNew Jersey, USASeptember 2005
 103 inproceedingsPotential for Discrimination in Online Targeted Advertising.FAT 2018  Conference on Fairness, Accountability, and Transparency81NewYork, United StatesFebruary 2018, 115
 104 inproceedingsPSINS: An Open Source Event Tracer and Execution Simulator for MPI Applications.EuroPar2009
 105 inproceedingsPrivacy Risks with Facebook’s PIIbased Targeting: Auditing a Data Broker’s Advertising Interface.39th IEEE Symposium on Security and Privacy (S&P)Proceedings of the 39th IEEE Symposium on Security and Privacy (S&P)San Francisco, United States2018
 106 inproceedingsCongestion Avoidance in LowVoltage Networks by using the Advanced Metering Infrastructure.ePerf 2018  IFIP WG PERFORMANCE  36th International Symposium on Computer Performance, Modeling, Measurements and EvalutionToulouse, FranceDecember 2018, 13
 107 inproceedingsDecentralized Optimization of Energy Exchanges in an Electricity Microgrid .ACM eEnergy 2016  7th ACM International Conference on Future Energy SystemsWaterloo, CanadaJune 2016
 108 inproceedingsDecentralized optimization of energy exchanges in an electricity microgrid.2016 IEEE PES Innovative Smart Grid Technologies Conference Europe (ISGTEurope)Ljubljana, SloveniaIEEEOctober 2016, 16
 109 inproceedingsScheduling for Reduced CPU Energy.Proceedings of the 1st USENIX Conference on Operating Systems Design and ImplementationOSDI '94USAMonterey, CaliforniaUSENIX Association1994, 2–es
 110 inproceedingsValidation and Uncertainty Assessment of ExtremeScale HPC Simulation through Bayesian Inference.EuroPar2013
 111 articleToward Scalable Performance Visualization with Jumpshot.International Journal of High Performance Computing Applications1331999
 112 inproceedingsBigSim: A Parallel Simulator for Performance Prediction of Extremely Large Parallel Machines.IPDPS2004
 113 unpublishedImproving the Performance of Batch Schedulers Using Online Job Runtime Classification.October 2020, Under review in JPDC