2023Activity reportProjectTeamPOLARIS
RNSR: 201622036M Research center Inria Centre at Université Grenoble Alpes
 In partnership with:Université de Grenoble Alpes, CNRS
 Team name: Performance analysis and Optimization of LARge Infrastructures and Systems
 In collaboration with:Laboratoire d'Informatique de Grenoble (LIG)
 Domain:Networks, Systems and Services, Distributed Computing
 Theme:Distributed and High Performance Computing
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, Researcher, HDR]
 Jonatha Anselmi [INRIA, Researcher]
 Nicolas Gast [INRIA, Researcher, HDR]
 Bruno Gaujal [INRIA, Senior Researcher, HDR]
 Panayotis Mertikopoulos [CNRS, Researcher, HDR]
 Bary Pradelski [CNRS, Researcher]
Faculty Members
 Romain Couillet [GRENOBLE INP, Professor]
 Vincent Danjean [UGA, Associate Professor]
 Guillaume Huard [UGA, Associate Professor]
 Florence Perronnin [UGA, Associate Professor, HDR]
 JeanMarc Vincent [UGA, Associate Professor]
 Philippe Waille [UGA, Associate Professor]
PostDoctoral Fellow
 Dheeraj Narasimha [INRIA, PostDoctoral Fellow, from Oct 2023]
PhD Students
 Sebastian Allmeier [INPG SA, from Nov 2023]
 Sebastian Allmeier [INRIA, until Oct 2023]
 Thomas Barzola [INPG SA, until Mar 2023]
 Achille Baucher [UGA]
 Victor Boone [UGA]
 Rémi Castera [UGA]
 Romain Cravic [INRIA]
 YuGuan Hsieh [UGA, until Sep 2023]
 Simon Jantschgi [CNRS, until May 2023]
 Kimang Khun [INRIA, until Mar 2023]
 Till Kletti [UGA, from Feb 2023 until Jun 2023]
 Till Kletti [NAVER LABS, until Feb 2023]
 Lucas Leandro Nesi [GOUV BRESIL]
 Hugo Lebeau [UGA]
 Davide Legacci [UGA]
 Victor Leger [UGA]
 Minh Toan Nguyen [INRIA, from Oct 2023]
 MinhToan Nguyen [INRIA]
 LouisSebastien Rebuffi [INRIA, from Oct 2023]
 LouisSebastien Rebuffi [UGA, until Sep 2023]
 Charles Sejourne [UGA]
Technical Staff
 Sacha Hodencq [FLORALIS, Engineer, until Mar 2023]
Interns and Apprentices
 PierreLouis Cauvin [INRIA, Intern, from Feb 2023 until Jul 2023]
 Mingming Dai [INRIA, Intern, from Feb 2023 until Aug 2023]
 Abel Douzal [INRIA, Intern, from Jun 2023 until Jul 2023]
 Apolline Rodary [INRIA, Intern, from Jun 2023 until Jul 2023]
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 propose 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 positioned with respect to this trend.
A first line of research in POLARIS is devoted to the use of 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. The resulting algorithms should not only learn an efficient (Nash) equilibrium but they should also be capable 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 human, 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 105, BSC 39, UIUC 114, Sandia Nat. Lab. 112, ORNL 40 or ETH Zürich 74) but most of them build 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, SMPI 48, 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 Geophysics application that suffers from spatial and temporal load balancing problem 78, 77 or the HPL benchmark 46, 47. We have shown that the performance (both for time and energy consumption 73) 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 92. 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 81, 115.
Trace Analysis and Visualization
Many monolithic visualization tools have been developed by renowned HPC groups since decades (e.g., BSC 96, Jülich and TU Dresden 91, 42, UIUC 72, 100, 76 and ANL 113) but most of these tools build on the classical information visualization 102 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/SPMD 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 56, 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 56 and more recently to a sparse direct solver 89. 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 developers. 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 executions.
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 41, 101 (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 instability) that had a significant effect on the nodes, from subtle performance changes of 1% to much more severe degradation 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 50, 49 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 forms 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 leads 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 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 that 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 58, 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 61, 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 63, 57.
Design and analysis of distributed control algorithms
Mean field approximation is widely used in the performance 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 44, 65, 64, we show how mean field and refined mean field approximation can be used to evaluate the performance of listbased cache replacement algorithms. In particular, we show that such policies can outperform the classically used LRU algorithm. A methodological 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 obtained 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 37, 38, 36, 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 37, 36 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 38 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 52, we develop the notion of discrete space mean field games, that is more amenable to study than the previously introduced notions of mean field games. This leads to two interesting contributions: mean field games are not always the limits of stochastic games as the number of players grow 51, mean field games can be used to study how much vaccination should be subsidized to encourage people to adapt a socially optimal behaviour 66.
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 67, 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 59.
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, 86, 84 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 43, 87, 88 suggested that strict Nash equilibria play an important role in this question. This suspicion was recently confirmed in a series of papers 55, 71 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 87, 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 75 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 104. 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) 45. 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 80, 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 54. 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 53, 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 106. 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) 35. A followup work shed further light on the typical uses of the platform 34. In another work, we proposed an innovative protocol based on randomized withdrawal to protect public posts deletion privacy 90. Finally, in 62, 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, 85 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 9782.
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 9995 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 98 and a vaccination policy 93). 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 94. 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 103. In fact, this is the reason why modern processors are equipped with Dynamic Voltage and Frequency Scaling (DVFS) technology 111. 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 69, 67, 68) as well as on the experimental side (showing the gains of optimal policies over classical solutions 70).
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 107, 109, 108, (2) how to cosimulate an electrical network and a communication network 79, and (3) what is the performance of the communication protocol (PLC G3) used by the Linky smart meters 83.
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 the research theme presented in Section 3.3.
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 continued 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 tool 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
We try to keep the carbon footprint of the team has low as possible by a stricter laptop renewal policy and by reducing plane travels (e.g., using visioconference or sometimes by avoiding publishing our research in conferences that would take place on the other side of the planet).
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.
5.2 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 several articles on the issue of "usability" of artificial intelligence. He is also cocreator of the sustainable AI transversal axis of the MIAI project in Grenoble. He connects his professionnal activity with public action (Lowtechlab de Grenoble, Université Autogérée, Arche des Innovateurs, etc). Finally, he is a trainer for the "Fresque du Climat" and a member of Adrastia and FNE Isère.
5.3 Impact of research results
JeanMarc Vincent is heavily engaged since several years in the training of computer science teachers at the elementary/middle/high school levels 33, 2. Among one of his many activities, we can mention his involvement in the design of the Numérique et Sciences Informatiques, NSI : les fondamentaux MOOC. See section 11.2.1 for more details.
6 Highlights of the year
6.1 Awards
Victor Boone and Panayotis Mertikopoulos have received a Spotlight at the NIPS conference for theeir article on The equivalence of dynamic and strategic stability under regularized learning in games 13.
7 New software, platforms, open data
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 simulation toolkit that provides core functionalities for the simulation of distributed applications in large scale heterogeneous distributed environments.

News of the Year:
There were 2 major releases in 2023. On modeling aspects, we released new plugins simulating chiller, photovoltaic and battery components of Fog/Edge infrastructures, as well as the disk arrays used in desegregated infrastructures. We improved the consistency of the simulation core: the new ActivitySet containers now make it easy to way for the completion of an heterogeneous set of activities (computation, communication, I/O, etc). The simulation of workflow and dataflow applications was also streamlined, with more examples, more documentation and less bugs. A new model of activities mixing disk I/O and network communication was introduced, to efficiently simulate accesses to remote disks. In addition, many efforts were put on the profiling of the software, leading to massive performance gains. We also pursued our efforts to improve the overall framework, through bug fixes, code refactoring and other software quality improvements. In particular, interfaces that were deprecated since almost a decade were removed to ease the maintenance burden on our community.
Many improvement occurred on the modelchecker side too. We dropped the old experiments toward stateful verification of liveness properties to boost the development of stateless verification of safety properties. Our tool is simpler internally, and usable on all major operating systems. We modernized the reduction algorithms, implementing several recent algorithms of the literature and paving the way to the introduction of new ones. We also introduced a new module allowing to verify not only distributed applications, but also threaded applications.
 URL:

Contact:
Martin Quinson

Participants:
Adrien Lebre, AnneCecile Orgerie, Arnaud Legrand, Augustin Degomme, Arnaud Giersch, Emmanuelle Saillard, Frédéric Suter, Jonathan Pastor, 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 a 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.
 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.
 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
 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.
 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, SIGMETRICS 2018, and a framework to compute heterogeneous mean field approximations as proposed in "Mean Field and Refined Mean Field Approximations for Heterogeneous Systems: It Works!" by N. Gast and S. Allmeier, SIGMETRICS 2022.
 URL:
 Publications:

Contact:
Nicolas Gast
8 New results
The new results produced by the team in 2023 can be grouped into the following categories.
8.1 Performance evaluation of Large Systems
Participants: Sebastian Allmeier, Thomas Barzola, Vincent Danjean, Arnaud Legrand, Nicolas Gast, Guillaume Huard, Lucas Leandro Nesi, JeanMarc Vincent.
Visualization strategies are a valuable tool in the performance evaluation of HPC applications. Although the traditional Gantt charts are a widespread and enlightening strategy, it presents scalability problems and may misguide the analysis by focusing on resource utilization alone. In 16, we propose an overview strategy to indicate nodes of interest for further investigation with classical visualizations like Gantt charts. For this, it uses a progression metric that captures work done per node inferred from the taskbased structure, a timestep clustering of those metrics to decrease redundant information, and a more scalable visualization technique. We demonstrate with six scenarios and two applications that such a strategy can indicate problematic nodes more straightforwardly while using the same visualization space. Also, we provide examples where it correctly captures application work progression, showing application problems earlier and as an easy way to compare nodes. At the same time that traditional methods are misleading.
This work completes our previous work on performance analysis of taskbased applications on heterogeneous platforms and is part of the PhD thesis of Lucas Leandro Nesi 27. It will be pursued in the WP5 (Performance analysis and prediction) of the ExaSoft pillar (High Performance Computing software and tools) of the PEPR NumPEx (Numérique Hautes Performances pour l'Exascale). The rest of the thesis of Lucas Leandro Nesi is more related to performance optimization (through algorithmic and reinforcement learning techniques) and evaluation (through predictive simulation and real experiments). A particular effort has been devoted to the reproducibility of the results through the opening of both the data, the code, and the underlying methodology.
Mean field approximation is a powerful technique which has been used in many settings to study largescale stochastic systems. Some of our latest developments have been transfered in the open source project rmf_tool7.1.6. In the case of twotimescale systems, the approximation is obtained by a combination of scaling arguments and the use of the averaging principle. In 1, we analyze the approximation error of this `average' mean field model for a twotimescale model $(\mathbf{X},\mathbf{Y})$, where the slow component $\mathbf{X}$ describes a population of interacting particles which is fully coupled with a rapidly changing environment $\mathbf{X}$. The model is parametrized by a scaling factor $N$, e.g. the population size, which as $N$ gets large decreases the jump size of the slow component in contrast to the unchanged dynamics of the fast component. We show that under relatively mild conditions, the `average' mean field approximation has a bias of order $O(1/N)$ compared to $\mathbb{E}\left[\mathbf{X}\right]$. This holds true under any continuous performance metric in the transient regime, as well as for the steadystate if the model is exponentially stable. To go one step further, we derive a bias correction term for the steadystate, from which we define a new approximation called the refined `average' mean field approximation whose bias is of order $O(1/{N}^{2})$. This refined `average' mean field approximation allows computing an accurate approximation even for small scaling factors, i.e., $N\approx $ 10 – 50. We illustrate the developed framework and accuracy results through an application to a random access CSMA model.
Finally, the PhD thesis of Thomas Barzola 22 presents a modular approach to compare optimization methods for bike sharing systems. Bike Sharing Systems (BSSs) are nowadays installed in many cities. In such a system, a user can take any available bike and return it to wherever there is an available parking spot. The Operations Research literature contains many papers that study optimization questions related to BSS, and in particular how to maximize the availability of bikes where and when the users need them. Yet, the optimization methods proposed by these papers are difficult to compare because most papers use their own problem instances and define their own metrics. This thesis aims to fill this gap by building a reproducible research methodology for BSSs. In this work, we divide this methodology in four modules: use of historical data, demand estimation, optimization methods, and performance evaluation. We study each module separately. In each case, we propose a prototype implementation and compare existing solutions when they are available.The first module handles the use of data from real systems. For many systems, two types of data are usually available: trips made by users, and records of the number of bikes available in each station. We observe that in general these data are inconsistent and we propose a method to correct this and detect relocation operations. The second module is the demand estimation one. In optimizing a BSS, it is essential to estimate the demand of the users for whom the system is designed. Most of the optimization works in the literature use historical demand to estimate the demand of the system. We experiment with the few existing methods of the literature along with a newly introduced method to detect censored demand. The third module is bike availability optimization. We implement a published optimization algorithm for this module as an example. We illustrate the challenges of reproducible research by trying to replicate the results. This chapter shows that, although the original authors made the data about their experiments available, we did not get the same quantitative results as the original publication. This difference highlights the need for better publication standards to produce more reproducible results. Finally, our fourth and last module is used to validate the optimization methods implemented in the 3rd module. We advocate that a simulator having all the requirements (user behavior models, demand scenarios, management strategies, etc.) can be a validation model. We use a thirdparty simulator to illustrate this module.We observe throughout this thesis that making research reproducible is not always handled with due diligence while being fundamental to produce valuable knowledge. In this work, we try our best efforts to specify and provide reproducible tools to ensure that researchers could obtain the same results with the same data. We give links to the data, codes, environments and analyses needed to reproduce the experiments.
8.2 Energy optimization
Participants: Jonatha Anselmi, Bruno Gaujal.
In 4, we optimize the scheduling of Deep Learning training jobs from the perspective of a Cloud Service Provider running a data center, which efficiently selects resources for the execution of each job to minimize the average energy consumption while satisfying time constraints. To model the problem, we first develop a MixedInteger NonLinear Programming formulation. Unfortunately, the computation of an optimal solution is prohibitively expensive, and to overcome this difficulty, we design a heuristic STochastic Scheduler (STS). Exploiting the probability distribution of early termination, STS determines how to adapt the resource assignment during the execution of the jobs to minimize the expected energy cost while meeting the job due dates. The results of an extensive experimental evaluation show that STS guarantees significantly better results than other methods in the literature, effectively avoiding due date violations and yielding a percentage total cost reduction between 32% and 80% on average. We also prove the applicability of our method in realworld scenarios, as obtaining optimal schedules for systems of up to 100 nodes and 400 concurrent jobs requires less than 5 seconds. Finally, we evaluated the effectiveness of GPU sharing, i.e., running multiple jobs in a single GPU. The obtained results demonstrate that depending on the workload and GPU memory, this further reduces the energy cost by 1729% on average.
8.3 Restless multiarmed bandits
Participants: Nicolas Gast, Bruno Gaujal, Kimang Kuhn, Chen Yan.
MultiArmed Bandits are a fundamental model for problems in which a decision maker has to iteratively select one of multiple fixed alternatives (i.e. arms or actions) when the reward of each choice is only partially known at the time of decision and is learned as as the decision maker interacts with the bandits. The regret of a strategy is the expectation of the sum of the collected rewards minus the expectation of the optimal reward (the one corresponding to the arm with the larger reward). Markov Decision Processes (MDP) provide a framework for modeling situations where the state of a system (and its associated reward) evolves partly random and partly under the control of the decision maker. The reward depends on the current state of the machine, but good policies can be computed (e.g., using dynamic programming although it can be computationally unreasonable) when the system is fully known upfront. We have considered the intermediate situation of restless and restful bandits where each arm corresponds to an independent Markov chain but where neither the chain nor the associated reward is initially knows. Each time a particular arm is played, the state of that chain advances to a new one, chosen according to the Markov state evolution probabilities. In the restless bandits problem, the states of nonplayed arms can also evolve over time.
Whittle index is a generalization of Gittins index that provides very efficient allocation rules for restless multiarmed bandits. In 5, we develop an algorithm to test the indexability and compute the Whittle indices of any finitestate restless bandit arm. This algorithm works in the discounted and nondiscounted cases, and can compute Gittins index. Our algorithm builds on three tools: (1) a careful characterization of Whittle index that allows one to compute recursively the $k$–th smallest index from the $(k1)$–th smallest, and to test indexability, (2) the use of the ShermanMorrison formula to make this recursive computation efficient, and (3) a sporadic use of the fastest matrix inversion and multiplication methods to obtain a subcubic complexity. We show that an efficient use of the ShermanMorrison formula leads to an algorithm that computes Whittle index in $O(2/3){n}^{3}+o\left({n}^{3}\right)$ arithmetic operations, where $n$ is the number of states of the arm. The careful use of fast matrix multiplication leads to the first subcubic algorithm to compute Whittle or Gittins index: By using the current fastest matrix multiplication, the theoretical complexity of our algorithm is $O\left({n}^{2.5286}\right)$. We also develop an efficient implementation of our algorithm that can compute indices of Markov chains with several thousands of states in less than a few seconds.
This work is part of the PhD thesis of Kimang Kuhn 25, where it was shown that no learning algorithms can perform uniformly well over the general class of restless bandits, and where several strategies for restful bandits have also been studied,
In 6, we evaluate the performance of Whittle index policy for restless Markovian bandit. It is shown in Weber and Weiss 110 that if the bandit is indexable and the associated deterministic system has a global attractor fixed point, then the Whittle index policy is asymptotically optimal in the regime where the arm population grows proportionally with the number of activation arms. In this paper, we show that, under the same conditions, this convergence rate is exponential in the arm population, unless the fixed point is singular, which almost never happens in practice. Our result holds for the continuoustime model of Weber and Weiss (1990) and for a discretetime model in which all bandits make synchronous transitions. Our proof is based on the nature of the deterministic equation governing the stochastic system: We show that it is a piecewise affine continuous dynamical system inside the simplex of the empirical measure of the arms. Using simulations and numerical solvers, we also investigate the singular cases, as well as how the level of singularity influences the (exponential) convergence rate. We illustrate our theorem on a Markovian fading channel model.
In 7, we also provide a framework to analyse control policies for the restless Markovian bandit model, under both finite and infinite time horizon. We show that when the population of arms goes to infinity, the value of the optimal control policy converges to the solution of a linear program (LP). We provide necessary and sufficient conditions for a generic control policy to be: i) asymptotically optimal; ii) asymptotically optimal with square root convergence rate; iii) asymptotically optimal with exponential rate. We then construct the LPindex policy that is asymptotically optimal with square root convergence rate on all models, and with exponential rate if the model is nondegenerate in finite horizon, and satisfies a uniform global attractor property in infinite horizon. We next define the LPupdate policy, which is essentially a repeated LPindex policy that solves a new linear program at each decision epoch. We provide numerical experiments to compare the efficiency of LPbased policies. We compare the performance of the LPindex policy and the LPupdate policy with other heuristics. Our result demonstrates that the LPupdate policy outperforms the LPindex policy in general, and can have a significant advantage when the transition matrices are wrongly estimated.
8.4 Reinforcement Learning and MDP
Participants: Jonatha Anselmi, Victor Boone, Romain Cravic, Nicolas Gast, Bruno Gaujal, LouisSébastien Rebuffi.
Although regret is a common objective in Reinforcement Learning, other criteria are relevant and allow to better understand or discriminate algorithms.
The first contribution of 12 is the introduction of a new performance measure of a RL algorithm that is more discriminating than the regret, that we call the regret of exploration that measures the asymptotic cost of exploration. The second contribution is a new performance test (PT) to end episodes in RL optimistic algorithms. This test is based on the performance of the current policy with respect to the best policy over the current confidence set. This is in contrast with all existing RL algorithms whose episode lengths are only based on the number of visits to the states. This modification does not harm the regret and brings an additional property. We show that while all current episodic RL algorithms have a linear regret of exploration, our method has a $O(logT)$ regret of exploration for nondegenerate deterministic MDPs.
In 11, we investigate a new learning problem, the identification of Blackwell optimal policies on deterministic MDPs (DMDPs): A learner has to return a Blackwell optimal policy with fixed confidence using a minimal number of queries. First, we characterize the maximal set of DMDPs for which the identification is possible. Then, we focus on the analysis of algorithms based on productform confidence regions. We minimize the number of queries by efficiently visiting the stateaction pairs with respect to the shape of confidence sets. Furthermore, these confidence sets are themselves optimized to achieve better performance. The performance of our method compares to the lower bound up to a factor ${n}^{2}$ in the worst case, where $n$ is the number of states, and constant in certain classes of DMDPs.
In 14, we propose the first modelfree algorithm that achieves low regret performance for decentralized learning in twoplayer zerosum tabular stochastic games with infinitehorizon averagereward objective. In decentralized learning, the learning agent controls only one player and tries to achieve low regret performances against an arbitrary opponent. This contrasts with centralized learning where the agent tries to approximate the Nash equilibrium by controlling both players. In our infinitehorizon undiscounted setting, additional structure assumptions is needed to provide good behaviors of learning processes : here we assume for every strategy of the opponent, the agent has a way to go from any state to any other. This assumption is the analogous to the "communicating" assumption in the MDP setting. We show that our Decentralized Optimistic Nash QLearning (DONQlearning) algorithm achieves both sublinear high probability regret of order 3/4 and sublinear expected regret of order 2/3. Moreover, our algorithm enjoys a low computational complexity and low memory space requirement compared to the previous works in the same setting.
Finally, in 30, we present an efficient reinforcement learning algorithm that learns the optimal admission control policy in a partially observable queueing network. Specifically, only the arrival and departure times from the network are observable, and optimality refers to the average holding/rejection cost in infinite horizon. While reinforcement learning in Partially Observable Markov Decision Processes (POMDP) is prohibitively expensive in general, we show that our algorithm has a regret that only depends sublinearly on the maximal number of jobs in the network, $\mathbf{S}$. In particular, in contrast with existing regret analyses, our regret bound does not depend on the diameter of the underlying Markov Decision Process (MDP), which in most queueing systems is at least exponential in $\mathbf{S}$. The novelty of our approach is to leverage Norton's equivalent theorem for closed productform queueing networks and an efficient reinforcement learning algorithm for MDPs with the structure of birthanddeath processes.
This work is part of the PhD thesis of LouisSebastien Rebuffi 29 and allows to propose reinforcement learning algorithms for controlled queueing systems that demonstrate a weak dependence on the state space compared to results obtained in the general case.
8.5 Learning in games
Participants: Victor Boone, YuGuan Hsieh, Panayotis Mertikopoulos.
Learning in games naturally occurs in situations where the resources or the decision is distributed among several agents or even in situations where a centralised decision maker has to adapt to strategic users. Yet, it 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.
A wide array of modern machine learning applications – from adversarial models to multiagent reinforcement learning – can be formulated as noncooperative games whose Nash equilibria represent the system's desired operational states. Despite having a highly nonconvex loss landscape, many cases of interest possess a latent convex structure that could potentially be leveraged to yield convergence to an equilibrium. Driven by this observation, we propose in 20 a flexible firstorder method that successfully exploits such "hidden structures" and achieves convergence under minimal assumptions for the transformation connecting the players' control variables to the game's latent, convexstructured layer. The proposed method – which we call preconditioned hidden gradient descent (PHGD) – hinges on a judiciously chosen gradient preconditioning scheme related to natural gradient methods. Importantly, we make no separability assumptions for the game's hidden structure, and we provide explicit convergence rate guarantees for both deterministic and stochastic environments.
In 13, we show the equivalence of dynamic and strategic stability under regularized learning in games by examining the longrun behavior of regularized, noregret learning in finite games. A wellknown result in the field states that the empirical frequencies of noregret play converge to the game's set of coarse correlated equilibria; however, our understanding of how the players' actual strategies evolve over time is much more limited  and, in many cases, nonexistent. This issue is exacerbated further by a series of recent results showing that only strict Nash equilibria are stable and attracting under regularized learning, thus making the relation between learning and pointwise solution concepts particularly elusive. In lieu of this, we take a more general approach and instead seek to characterize the setwise rationality properties of the players' daytoday play. To that end, we focus on one of the most stringent criteria of setwise strategic stability, namely that any unilateral deviation from the set in question incurs a cost to the deviator  a property known as closedness under better replies (club). In so doing, we obtain a farreaching equivalence between strategic and dynamic stability: a product of pure strategies is closed under better replies if and only if its span is stable and attracting under regularized learning. In addition, we estimate the rate of convergence to such sets, and we show that methods based on entropic regularization (like the exponential weights algorithm) converge at a geometric rate, while projectionbased methods converge within a finite number of iterations, even with bandit, payoffbased feedback.
In 3, we examine the longrun behavior of multiagent online learning in games that evolve over time. Specifically, we focus on a wide class of policies based on mirror descent, 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., when players only get to observe the payoffs of their chosen actions.
In 9, we develop a flexible stochastic approximation framework for analyzing the longrun behavior of learning in games (both continuous and finite). The proposed analysis template incorporates a wide array of popular learning algorithms, including gradientbased methods, the exponential / multiplicative weights algorithm for learning in finite games, optimistic and bandit variants of the above, etc. In addition to providing an integrated view of these algorithms, our framework further allows us to obtain several new convergence results, both asymptotic and in finite time, in both continuous and finite games. Specifically, we provide a range of criteria for identifying classes of Nash equilibria and sets of action profiles that are attracting with high probability, and we also introduce the notion of coherence, a gametheoretic property that includes strict and sharp equilibria, and which leads to convergence in finite time. Importantly, our analysis applies to both oraclebased and bandit, payoffbased methods – that is, when players only observe their realized payoffs.
This work is part of the PhD thesis of Yu Guan Hsieh 23 entitled DecisionMaking in multiagent systems: delays, adaptivity, and learning in games, and which has investigated separately two critical aspects of multiagent systems: the impact of delays and the interactions among agents with nonaligned interests.
8.6 Quantum Games
Participants: Panayotis Mertikopoulos.
Although the games we generally consider for learning have nothing to do with the quantum world, they often involve probabilities (to account for the uncertainty of the agents or of the nature) and semidefinite programming (e.g., when dealing with the optimization of MIMO antennas). Quantum games have thus been a natural target for which we have proposed several contributions.
Recent developments in domains such as nonlocal games, quantum interactive proofs, and quantum generative adversarial networks have renewed interest in quantum game theory and, specifically, quantum zerosum games. Central to classical game theory is the efficient algorithmic computation of Nash equilibria, which represent optimal strategies for both players. In 2008, Jain and Watrous proposed the first classical algorithm for computing equilibria in quantum zerosum games using the Matrix Multiplicative Weight Updates (MMWU) method to achieve a convergence rate of $O(d/{\epsilon}^{2})$ iterations to $\epsilon $Nash equilibria in the $4d$dimensional spectraplex. In 21, we propose a hierarchy of quantum optimization algorithms that generalize MMWU via an extragradient mechanism. Notably, within this proposed hierarchy, we introduce the Optimistic Matrix Multiplicative Weights Update (OMMWU) algorithm and establish its averageiterate convergence complexity as $O(d/\epsilon )$ iterations to $\epsilon $Nash equilibria. This quadratic speedup relative to Jain and Watrous' original algorithm sets a new benchmark for computing $\epsilon $Nash equilibria in quantum zerosum games.
In 17, we study the problem of learning in quantum games and other classes of semidefinite gameswith scalar, payoffbased feedback. For concreteness, we focus on the widely used matrix multiplicative weights (MMW) algorithm and, instead of requiring players to have full knowledge of the game (and/or each other's chosen states), we introduce a suite of minimalinformation matrix multiplicative weights (3MW) methods tailored to different information frameworks. The main difficulty to attaining convergence in this setting is that, in contrast to classical finite games, quantum games have an infinite continuum of pure states (the quantum equivalent of pure strategies), so standard importanceweighting techniques for estimating payoff vectors cannot be employed. Instead, we borrow ideas from bandit convex optimization and we design a zerothorder gradient sampler adapted to the semidefinite geometry of the problem at hand. As a first result, we show that the 3MW method with deterministic payoff feedback retains the $O(1/\sqrt{T})$ convergence rate of the vanilla, full information MMW algorithm in quantum minmax games, even though the players only observe a single scalar. Subsequently, we relax the algorithm's information requirements even further and we provide a 3MW method that only requires players to observe a random realization of their payoff observable, and converges to equilibrium at an $O\left({T}^{1/4}\right)$ rate. Finally, going beyond zerosum games, we show that a regularized variant of the proposed 3MW method guarantees local convergence with high probability to all equilibria that satisfy a certain firstorder stability condition.
Finally, in 18, we study the equilibrium convergence and stability properties of the widely used matrix multiplicative weights (MMW) dynamics for learning in general quantum games. A key difficulty in this endeavor is that the induced quantum state dynamics decompose naturally into (i) a classical, commutative component which governs the dynamics of the system's eigenvalues in a way analogous to the evolution of mixed strategies under the classical replicator dynamics; and (ii) a noncommutative component for the system's eigenvectors. This noncommutative component has no classical counterpart and, as a result, requires the introduction of novel notions of (asymptotic) stability to account for the nonlinear geometry of the game's quantum space. In this general context, we show that (i) only pure quantum equilibria can be stable and attracting under the MMW dynamics; and (ii) as a partial converse, pure quantum states that satisfy a certain "variational stability" condition are always attracting. This allows us to fully characterize the structure of quantum Nash equilibria that are stable and attracting under the MMW dynamics, a fact with significant implications for predicting the outcome of a multiagent quantum learning process.
8.7 Continuous optimization methods
Participants: YuGuan Hsieh, Panayotis Mertikopoulos.
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.
Many modern machine learning applications – from online principal component analysis to covariance matrix identification and dictionary learning – can be formulated as minimization problems on Riemannian manifolds, and are typically solved with a Riemannian stochastic gradient method (or some variant thereof). However, in many cases of interest, the resulting minimization problem is not geodesically convex, so the convergence of the chosen solver to a desirable solution – i.e., a local minimizer – is by no means guaranteed. In 15, we study precisely this question, that is, whether stochastic Riemannian optimization algorithms are guaranteed to avoid saddle points with probability 1. For generality, we study a family of retractionbased methods which, in addition to having a potentially much lower periteration cost relative to Riemannian gradient descent, include other widely used algorithms, such as natural policy gradient methods and mirror descent in ordinary convex spaces. In this general setting, we show that, under mild assumptions for the ambient manifold and the oracle providing gradient information, the policies under study avoid strict saddle points / submanifolds with probability 1, from any initial condition. This result provides an important sanity check for the use of gradient methods on manifolds as it shows that, almost always, the limit state of a stochastic Riemannian algorithm can only be a local minimizer.
In 31, we examine the lastiterate convergence rate of Bregman proximal methods  from mirror descent to mirrorprox and its optimistic variants  as a function of the local geometry induced by the proxmapping defining the method. For generality, we focus on local solutions of constrained, nonmonotone variational inequalities, and we show that the convergence rate of a given method depends sharply on its associated Legendre exponent, a notion that measures the growth rate of the underlying Bregman function (Euclidean, entropic, or other) near a solution. In particular, we show that boundary solutions exhibit a stark separation of regimes between methods with a zero and nonzero Legendre exponent: the former converge at a linear rate, while the latter converge, in general, sublinearly. This dichotomy becomes even more pronounced in linearly constrained problems where methods with entropic regularization achieve a linear convergence rate along sharp directions, compared to convergence in a finite number of steps under Euclidean regularization.
8.8 Random matrix analysis and Machine Learning
Participants: Romain Couillet, MinhToan Nguyen.
Random matrix theory has recently proven to be a very effective tool to understand Machine Learning challenges. In particular, concentration results can be used to derive more efficient and frugal algorithms.
The PhD thesis of MinhToan Nguyen 28 has provided a nice overview with a deep perspective on replica method and asymptotic equivalence. Replica method is a favorite tool of physicists for studying large disordered systems. Although the method is highly nonrigorous, it can solve difficult problems across various domains: random matrix theory, convex optimization, combinatorial optimization, Bayesian inference, etc. The method has been successfully used to analyze theoretical models in wireless communication and machine learning. The rigorous alternatives for the replica method include the method of deterministic equivalents in random matrix theory, the objective method in combinatorial optimization, and the CGMT (convex Gaussian minmax theorem) in random convex optimization. Although these methods works in different domains, they offer one common insight: the asymptotic equivalence, which tells us that the large system under study is equivalent to a simpler system. As a result, many difficult computations on the original system can be done more easily on the equivalent system. In contrast, with the replica method, the insights come after the calculations. We start by writing down what we want to compute and then proceed to get the answer at the end. After calculating various quantities related to the system, with some observations and a good intuition, we may uncover the equivalent system. In this thesis, we show that the asymptotic equivalent of a disordered system can be obtained directly through the replica formalism by paying attention to the largedeviation computations lurking behind the replica computations. In other words, we develop a version of the replica method that can directly compute the asymptotic equivalent of a disordered system. This version of the replica method, which fits into the same framework of deterministic equivalence as the rigorous methods above, can compute the deterministic equivalents of random matrices, formally derive the CGMT, and solve problems in highdimensional Bayesian statistics. Moreover, it can derive results on the SherringtonKirkpatrick model in a clear and simple manner. In this version of the replica method, each disordered system is associated with an object called “the replica density”. By De Finetti's theorem, a disordered system can be recovered from its replica density. To compute the asymptotic equivalent of a disordered system, we compute the equivalent of its replica density, using a result that we derive from the fundamental Gibbs principle. We thus obtain another replica density, which corresponds to another disordered system. This system is asymptotically equivalent to the original disordered system.
8.9 Fairness and equity in digital (recommendation, advertising, persistent storage) systems
Participants: Rémi Castera, Nicolas Gast, Till Kletti, Simon Jantschgi, Mathieu Molina, Bary Pradelski.
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. In this context, fairness, discrimination, and privacy are particularly important issues.
In 32, we study statistical discrimination in matching, where multiple decisionmakers are simultaneously facing selection problems from the same pool of candidates. We propose a model where decisionmakers observe different, but correlated estimates of each candidate's quality. The candidate population consists of several groups that represent gender, ethnicity, or other attributes. The correlation differs across groups and may, for example, result from noisy estimates of candidates' latent qualities, a weighting of common and decisionmaker specific evaluations, or different admission criteria of each decision maker. We show that lower correlation (e.g., resulting from higher estimation noise) for one of the groups worsens the outcome for all groups, thus leading to efficiency loss. Further, the probability that a candidate is assigned to their first choice is independent of their group. In contrast, the probability that a candidate is assigned at all depends on their group, and — against common intuition — the group that is subjected to lower correlation is better off. The resulting inequality reveals a novel source of statistical discrimination.
In 8, we conducted a large number of controlled continuous double auction experiments to reproduce and stresstest the phenomenon of convergence to competitive equilibrium under private information with decentralized trading feedback. Our main finding is that across a total of 104 markets (involving over 1,700 subjects), convergence occurs after a handful of trading periods. Initially, however, there is an inherent asymmetry that favors buyers, typically resulting in prices below equilibrium levels. Analysis of over 80,000 observations of individual bids and asks helps identify empirical ingredients contributing to the observed phenomena including higher levels of aggressiveness initially among buyers than sellers.
This work is part of the PhD thesis of Simon Jantschgi 24 on market design for double auctions.
Individual behavior such as choice of fashion, adoption of new products, and selection of means of transport is influenced by taking account of others' actions. In 10, we study social influence in a heterogeneous population and analyze the behavior of the dynamic processes. We distinguish between two information regimes: (i) agents are influenced by the adoption ratio, (ii) agents are influenced by the usage history. We identify the stable equilibria and longrun frequencies of the dynamics. We then show that the two processes generate qualitatively different dynamics, leaving characteristic 'footprints'. In particular, (ii) favors more extreme outcomes than (i).
In 19, we consider the problem of online allocation subject to a longterm fairness penalty. Contrary to existing works, however, we do not assume that the decisionmaker observes the protected attributes – which is often unrealistic in practice. Instead they can purchase data that help estimate them from sources of different quality; and hence reduce the fairness penalty at some cost. We model this problem as a multiarmed bandit problem where each arm corresponds to the choice of a data source, coupled with the online allocation problem. We propose an algorithm that jointly solves both problems and show that it has a regret bounded by $O\left(\sqrt{T}\right)$. A key difficulty is that the rewards received by selecting a source are correlated by the fairness penalty, which leads to a need for randomization (despite a stochastic setting). Our algorithm takes into account contextual information available before the source selection, and can adapt to many different fairness notions. We also show that in some instances, the estimates used can be learned on the fly.
Finally, fairness has also been studied in the PhD thesis of Till Kletti 26, in the context of multistakeholder recommendation platforms. The object of study of this thesis is the ranking of potentially relevant objects in response to an information request, for example when using a search engine or in the case of online content recommendation. Such a ranking brings together two groups: users searching for relevant information, and content producers, whose goal is to make the produced information visible.For example, when searching for restaurants, the user is interested in seeing good restaurants,while the interest of the restaurant owners is to be seen by many people, in order to attract customers. The objects to be ranked are thus competing with each other and it is in the interest of the platform generating the rankings to ensure that the exposure allocated to the objects is fairly distributed. Obviously there are many possibilities of defining what fair means and none of them will be unanimously agreed upon. Therefore in this thesis the definition of fairness is taken as a parameter represented by a vector of merit, which determines the proportion with which visibility should be distributed amongst the items. This will make our method applicable to a wide range of possible definitions.Two things then become apparent. First, there does not in general exists ranking that is fair in the sense of proportionality of exposure to merit. It is therefore necessary to produce several rankings that compensate each other in order to give, on average, fair exposures to the items.Secondly, these rankings do not generally give maximum utility to the user. Indeed, to guarantee fairness, less relevant objects could potentially be shown to him. These two objectives, fairness and utility, are thus not simultaneously optimizable. The contribution of this thesis is to develop methods to determine Pareto optimal ranking sequences, i.e. such that it is not possible to improve one of the two objectives without deteriorating the other. The idea is that this would make it possible for a qualified decision maker to make an informed choice about an adequate tradeoff between user utility and fairness amongst items.The determination of these optimal sequences is accomplished via the introduction of a geometric object, a polytope named expohedron. This polytope expresses the set of average exposures attainable with ranking sequences and is therefore a good decision space for both fairnessand utility. The expohedron makes it possible to compute these optimal ranking sequences using only mathematically exact geometric constructions inside it, and this in a significantly faster way than previous methods based on linear programming. Moreover, the proposed method is applicable to two large classes of exposure models including Position Based Model (PBM) and Dynamic Bayesian Network (DBN) models to which linear programming is not applicable.
9 Bilateral contracts and grants with industry
Participants: HenryJoseph Audéoud, Till Kletti, Nicolas Gast, 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.
Nicolas Gast obtained a grant from Enedis to evaluate the performance of the PLCG3 protocol. This grant supported the postdoc of HenryJoseph Audeoud.
10 Partnerships and cooperations
10.1 European initiatives
10.1.1 Other european programs/initiatives
Participants: Arnaud Legrand.

Unite!
Arnaud Legrand is involved in the WP6 (Open Science) of the Unite! (University Network for Innovation, Technology and Engineering) project , which aims to create a large European campus from Finland to Portugal. Unite! brings together 7 partners, recognized for the quality of their education and research: Technische Universität Darmstadt (Germany), Aalto University (Finland), Kunglia Tekniska Hoegskolan (Sweden), Politecnico di Torino (Italy), Universitat Politecnica de Catalunya (Spain), Universidade de Lisboa (Portugal) and Grenoble INP, Graduate Schools of Engineering and Management, Université Grenoble Alpes.
10.2 National initiatives
Projects indicated with a $\u2606$ are projects coordinated by members of the POLARIS team.
ANR

ANR ALIAS (PRCI 20202023)$\u2606$
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 of 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.
IRS/UGA

UGA MIAI Chaire (20192023)$\u2606$
[365K€] Patrick Loiseau is in charge of the Explainable and Responsible AI chaire of the MIAI institute. To build more trustworthy AI systems, we investigate how to produce explanations for results returned by AI systems and how to build AI algorithms with guarantees of fairness and privacy, in the setting of varied tasks such as classification, recommendation, resource allocation or matching.
11 Dissemination
11.1 Promoting scientific activities
11.1.1 Scientific events: organisation
 Member of the organizing committees
 Nicolas Gast , Aditya Mahajan, and Annie Simon have organized the Workshop on restless bandits, index policies and applications in reinforcement learning in Grenoble, France, November 2023, which has attracted about 40 researchers of the domain from all over Europe. This event was coorganized with the support of the GDR COSMOS.
 Arnaud Legrand coorganized with five other colleagues the first Meeting days of the French network for reproducible research in Paris, France, March 2023, which has attracted about a hundred of researchers. The aim of these days was to provide an overview of the state of reproducibility in scientific research in France, taking into account the diversity of disciplines and practices.
 JeanMarc Vincent has coorganized the Colloque de la SIF: le système dans tous ses états in Grenoble, April 2023.
 General chair, scientific chair
 Panayotis Mertikopoulos coorganized the 2023 thematic program on Games, Learning, and Networks in Singapore, from April 3 to April 21, 2023. This program brought together around 80 researchers in total, with the aim of studying emerging questions on game theory and its applications.
 Panayotis Mertikopoulos , Bruno Gaujal , and Annie Simon coorganized the 2023 Alpine Game Theory Symposium in Grenoble, from June 26 to June 30, 2023. This symposium brought together about 100 researchers working on all aspects of game theory (mathematical, economic, algorithmic, etc.), with the aim of fostering collaborations and interactions between the various communities. It was primarily sponsored by the French Game Theory Society, Inria, MIAI, and the ANR project ALIAS.
11.1.2 Scientific events: selection
 Member of the conference program committees
 Jonatha Anselmi was a PC member of the Algorithms Track for ICPP 2023.
 Bruno Gaujal was member of the following TPC: ICML, Mascots, and NeurIPS.
 Nicolas Gast was member of the Technical Program Committee of Sigmetrics 2024 and ICLR 2023.
 Panayotis Mertikopoulos served as an area chair for ICLR 2023, ICML 2023, and NeurIPS 2023.
 Reviewer
 Panayotis Mertikopoulos served as a reviewer for COLT 2023.
11.1.3 Journal
 Member of the editorial boards
 Nicolas Gast is associate editor of Performance Evaluation, Stochastic Models and TMLR.
 Panayotis Mertikopoulos served as an associate editor for Operations Research Letters, EURO Journal on Computational Optimization, Methodology and Computing in Applied Probability, and the Journal on Dynamics and Games.
 Since December 2023, Panayotis Mertikopoulos is an associate editor for Mathematics of Operations Research, and the managing coeditor for the Open Journal of Mathematical Optimization.
 Reviewer  reviewing activities
 Jonatha Anselmi was a reviewer for Mathematics of Operation Research, IEEE Transactions on Parallel and Distributed Systems, Queueing Systems, Performance Evaluation.
 Bruno Gaujal was a reviewer for MOR.
 Panayotis Mertikopoulos reviewed around 10 papers for various journals in mathematical optimization and game theory.
11.1.4 Invited talks

Bruno Gaujal
was invited to present his work at the following events:
 ROADEF as a plenary speaker, at Rennes (Feb. 2023): Reinforcement Learning and Markovian Bandits
 Seminaire Parisien d’Optimisation (April 2023): Higher Order Reinforcement Learning
 OR Seminar, at Univ. of Porto (June 2023): Reinforcement Learning in Markov Decision Processes
 Informs Applied Probability Society, at Nancy (June 2023): Reinforcement Learning
 EDF R&D Seminar, (Oct. 2023): Learning Indexes in Rested Bandits
 LAAS Seminar, Toulouse, (Nov. 2023): Learning Optimal Admission Control in Partially Observable Queueing Networks
 Nicolas was invited to present his work at the following events:
 EDF R&D: MeanField Control for Restless Bandits and Weakly Coupled MDPs
 Inria Paris, workshop "8 days on Network Mathematics": Approximations for dynamics on graphs
 Cornell OREI: MeanField Control for Restless Bandits and Weakly Coupled MDPs
 Online CNI seminar series: MeanField Control for Restless Bandits and Weakly Coupled MDPs
 Université Laval (Québec): The bias of mean field approximation
 McGuill university (Montreal): How to Use MeanField Control for Restless Bandits and Weakly Coupled MDPs

Arnaud Legrand
was invited to give lectures and keynotes on Reproducible Research and Open Science on the following occasions:
 M1 students in computer science at UGA (Dec. 2023): Reproducible Research and Computer Science
 Neurocampus Open Science Workshop at Bordeaux (Oct. 2023): Good practices in the lab: Research documentation and electronic notebooks
 New Inria PhD students at Grenoble (Oct. 2023): Doing a PhD, good practice and pitfalls to avoid
 Inria foresight seminar of the Optimization, Machine Learning and Statistical Methods theme at Rungis (Oct. 2023): Reproducible Research and Benchmarking
 Colloque de la MITI Réplicabilité/reproductibilité de la recherche : enjeux et propositions at Paris (Sep. 2023): Réplicabilité et reproductibilité de la recherche: Impact sur les pratiques des chercheuses et chercheurs
 Journée GitLab, GT ”Données” de la MITI du CNRS at Paris (June 2023): Scientific Data Management with Git and GitAnnex
 MaiMosine, GRICAD, SARI network, remote conference (June 2023): Laboratory notebook, computational document, reproducible article. Emacs/Orgmode: One ring to rule them all?
 Journées scientifiques de l'équipe AVALON at Le Sapey (June 2023): Reproducible Research and Computer Science
 20th Anniversary of Grid'5000 at Lyon (May 2023): Reproducible Research and Computer Science
 Réseau des référents science ouverte à la CPU, remote conference (March 2023): Formation à grande échelle à la Recherche Reproductible
 Master2 Mathématiques, Vision, Apprentissage at Saclay (March 2023): Reproducibility Crisis, Open Science,… and Computer Science
 1ères Journées du Réseau National Recherche reproductible at Paris (March 2023): Formation à grande échelle à la Recherche Reproductible
 Unite! Dialogue, remotely (March 2023): CNRS Open Science policy
 Seminar at the AG of the LISTIC, at Annecy (Feb. 2023): Reproducibility Crisis, Open Science,… and Computer Science

Panayotis Mertikopoulos
was invited to give a tutorial at the following events:
 NTUA Summer School on the Mathematics of Machine Learning, Athens, GR: Optimization algorithms for machine learning

Panayotis Mertikopoulos
was invited to give a talk in the following conferences:
 Conference in honor of Roberto Cominetti's 60th birthday, Viña del Mar, CL: Adaptive routing in largescale networks
 Workshop in honor of Elias Koutsoupias' 60th birthday, Athens, GR: The attractors of regularized learning in games
 2023 Athens Colloquium on Algorithms and Complexity, Athens, GR: Strategic stability under regularized learning

Panayotis Mertikopoulos
was invited to give a talk in the following universities and research institutes:
 University of Athens, Athens, GR: Adaptive routing under uncertainty
 DeepMind, London, UK: Accelerated and optimistic methods for learning
 University of Athens, Athens, GR: From Robbins–Monro to artificial intelligence: 70 years of stochastic approximation
 TII, online: Training models with a minmax landscape
 Mannheim University, Mannheim, DE: A stochastic approximation framework for multiagent learning
11.1.5 Leadership within the scientific community
 Vincent Danjean , Guillaume Huard , Arnaud Legrand , and JeanMarc Vincent, are involved in the WP5 (Performance analysis and prediction) of the ExaSoft pillar (High Performance Computing software and tools) of the PEPR NumPEx (Numérique Hautes Performances pour l'Exascale).
 Panayotis Mertikopoulos is the scientific coordinator of the PEPR IA projet ciblé (acceleration grant) FOUNDRY: Foundations of robustness and reliability in artificial intelligence. The project has a total budget of 5M€ and involves five research teams across France (POLARIS in Grenoble, the Inria teams SCOOL and FAIRPLAY, Dauphine and IMT in Paris, and ENS Lyon).
11.1.6 Research administration
 Vincent Danjean is a member of the Conseil d'Administration of GrenobleINP.
 Nicolas Gast is vicedirector of the école doctorale MSTII.
 Arnaud Legrand is a member of the Section 6 of the CoNRS.
 Arnaud Legrand is head of the SRCPR axis of the LIG and a member of LIG bureau.
 Arnaud Legrand is a member of Comité Scientique of the Inria Grenoble.
 Florence Perronin is a member of the QVT team of the LIG.
11.2 Teaching  Supervision  Juries
11.2.1 Teaching
 Jonatha Anselmi teaches Probabilités et simulation (32h) and Évaluation de performances (32h) at PolyTech Grenoble.
 Vincent Danjean teaches the Operating Systems, Programming Languages, Algorithms, Computer Science and Mediation lectures in L3, M1 and Polytech Grenoble.
 Vincent Danjean organized with J.M. Vincent a complementary training for high school professors to teach computer science.
 Nicolas Gast teaches the Reinforcement learning part of the M2 course Mathematical foundations of machine learning at the M2 MOSIG (Grenoble).
 Bruno Gaujal and Nicolas Gast teach Markov Decision Process and Reinforcement Learning (32h in total) at the M2 Info (ENS Lyon).
 Bruno Gaujal teaches Optimisation under uncertainties (18h) at the M2 ORCO (UGA).
 Guillaume Huard is responsible of L3 Info and of the Licence Info.
 Guillaume 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.
 Arnaud Legrand and JeanMarc Vincent teach the transversal Scientific Methodology and Empirical Evaluation lecture (36h) at the M2 MOSIG (UGA).
 The 3rd edition of the MOOC of Arnaud 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 2024), more than 20,800 persons have followed this MOOC and about 2100 certificates of achievement have been delivered. More than half of participants are PhD students and about 10% are undergraduates.
 Florence Perronin teaches Programming Languages in L1.
 Florence Perronin is a member of the conseil de perfectionnement of the Mathematics license.
 JeanMarc Vincent contributed to the MOOC NSI: Introduction à la préparation au CAPES NSI, pour les futurs enseignants de lycée en informatique.
 Panayotis Mertikopoulos teaches a graduate course in game theory in the University of Athens.
11.2.2 Supervision
 Arnaud Legrand was a member of the Comité de Suivi Individuel of Adeyemi Adetula (UGA)
 Panayotis Mertikopoulos is cosupervising two PhD students in addition of the ones in POLARIS (Victor Boone and Davide Legacci): : Waïss Azizian and PierreLouis Cauvin, both with Jérôme Malick (LJK).
11.2.3 Juries
 Nicolas Gast was a reviewer of the PhD committee of Aymen Al Mariani (Ens de Lyon): Adaptive Pure Exploration in Markov Decision Processes and Bandits.
 Nicolas Gast was a member of the PhD jury of Michel Davydov (Ens Paris): Pointprocessbased Markovian dynamics and their applications.
 Bruno Gaujal was a member of the PhD thesis committee of Aymen Al Marjani (ENS Lyon): Adaptive Pure Exploration in Markov Decision Processes and Bandits.
 Bruno Gaujal was a reviewer for the HDR of Balakrishna Prabhu (Univ. Toulouse): Some applications of asymptotic analysis in communication networks.
 Bruno Gaujal was a member of the PhD thesis committee of Fabien Pesquerel (Univ. Lille): Information par unité d'interaction dans la prise de décisions séquentielles en environnement stochastique.
 Arnaud Legrand was a reviewer for the HDR of Guillaume Pallez (Univ. Bordeaux): Model Design and Accuracy for Resource Management in HPC.
 Arnaud Legrand was a member of the PhD thesis committee of Julien Emmanuel (Univ. Lyon): Un simulateur pour le calcul haute performance : modélisation multiniveau de l'interconnect BXI pour prédire les performances d'applications MPI.

Panayotis Mertikopoulos
was a reviewer / external examiner for the PhD theses of:
 Le Cong Dinh (U. Southampton): Online Learning in the Presence of Strategic Adversary
 Simon Jantschgi (ETH Zürich / UGA): Market Design for Double Auctions
 Lucas Baudin (ParisDauphine): Contributions to Online Learning in Stochastic Games
 Étienne de Montbrun (Toulouse 1 Capitole): Game Theory and Online Learning: Gradient Descent Ascent, Optimization, Approximation and Certification
 Maurizio d'Andrea (Toulouse 1 Capitole): Learning Algorithms in GameTheoretic Contexts

Panayotis Mertikopoulos
was an examiner for the PhD theses of:
 Rémi Leluc (IP Paris): Monte Carlo Methods and Stochastic Approximation: Theory and Applications to Machine Learning
 Vicky Kouni (U. Athens): Modelbased and datadriven approaches meet redundancy in signal processing
11.3 Popularization
11.3.1 Articles and contents
We have contributed to a Frenchspeaking teacher training center dedicated to computer science education in high school.
 The introduction of computer science education in high school will allow the next generations to master and participate in the development of digital technology. The main issue is therefore the training of teachers. We are helping to meet this challenge by forming a community of learning and practice with the welcome and support of hundreds of colleagues in activity or in training and by offering two online training courses, one regarding the fundamentals of computer science, with resources for initiation and improvement the other to learn to teach by doing, by copreparing the educational activities of the courses to come, by sharing didactic practices and by taking a pedagogical step back, including from the point of view of the pedagogy of equality, supplemented by hybrid initiatives. We share in 33 the approach and the analysis from the point of view of educational sciences of the first results obtained. In terms of research, what we are presenting here falls within the framework of what is called "research within action".
 In many European countries, we're starting to teach our children not just how to use digital technology, but how to understand its fundamentals so they can master it. At the same time, we need to train part of our future population in the discipline of computing, which is both a science and a technique, and which can be found as a fundamental skill in all fields that have become digital. The key issue here is teacher training. We help to meet this challenge with a dual online training program, one for the fundamentals of computing, with introductory and advanced resources, and the other for learning to teach by doing, by copreparing the pedagogical activities of future courses, and sharing teaching practices. This includes pedagogical hindsight, including from the point of view of equality pedagogy. This resource enables a community of learning and practice to be formed, with hundreds of colleagues in training or already in work welcoming and helping each other. This is complemented by hybrid initiatives across the region. In 2, we share our approach and analyze the initial results from an educational science perspective, showing just how valuable the links between teaching and research can be at this level.
11.3.2 Education
 Florence Perronin has set up a program to promote mental health for L3 Maths students.
 Florence Perronin has been a member of the committee of Journées de l'innovation en promotion de la santé mentale (sep. 2023).
 Guillaume Huard is a member of the development team of Caseine.
12 Scientific production
12.1 Publications of the year
International journals
 1 articleBias and Refinement of Multiscale Mean Field Models.Proceedings of the ACM on Measurement and Analysis of Computing Systems 712023, 129HALDOIback to text
 2 articleUn espace de formation francophone des enseignants, dédié à l’apprentissage de l’informatique, dans le secondaire.Adjectif : analyses et recherches sur les TICENovember 2023HALback to textback to text
 3 articleMultiagent online learning in timevarying games.Mathematics of Operations Research4822023, 914941HALDOIback to text
 4 articleA Stochastic Approach for Scheduling AI Training Jobs in GPUbased Systems.IEEE Transactions on Cloud Computing2023, 117HALDOIback to text
 5 articleTesting Indexability and Computing Whittle and Gittins Index in Subcubic Time.Mathematical Methods of Operations ResearchJune 2023HALDOIback to text
 6 articleExponential Asymptotic Optimality of Whittle Index Policy..Queueing Systems104June 2023, 144HALDOIback to textback to text
 7 articleLPbased policies for restless bandits: necessary and sufficient conditions for (exponentially fast) asymptotic optimality.Mathematics of Operations ResearchDecember 2023HALDOIback to textback to text
 8 articleCOMPETITIVE MARKET BEHAVIOR: CONVERGENCE AND ASYMMETRY IN THE EXPERIMENTAL DOUBLE AUCTION.International Economic Review6432023, 1087  1126HALDOIback to text
 9 articleA unified stochastic approximation framework for learning in games.Mathematical ProgrammingAugust 2023, 140HALDOIback to text
 10 articleSocial influence: The Usage History heuristic.Mathematical Social SciencesMay 2023HALback to text
International peerreviewed conferences
 11 inproceedingsIdentification of Blackwell Optimal Policies for Deterministic MDPs.Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, PMLRAISTATS 2023  26th International Conference on Artificial Intelligence and Statistics206Valencia, SpainApril 2023, 32HALback to text
 12 inproceedingsThe Regret of Exploration and the Control of Bad Episodes in Reinforcement Learning.PMLRICML 2023  40th International Conference on Machine Learning202HawaiiHonolulu, United StatesJuly 2023, 28242856HALback to text
 13 inproceedingsThe equivalence of dynamic and strategic stability under regularized learning in games.Proceedings of the 37th International Conference on Neural Information Processing SystemsNeurIPS 2023  37th Conference on Neural Information Processing SystemsNew Orleans (LA), United StatesNovember 2023, 131HALback to textback to text
 14 inproceedingsDecentralized modelfree reinforcement learning in stochastic games with averagereward objective.AAMAS 2023  International Conference on Autonomous Agents and Multiagent SystemsLondon (U.K.), United KingdomJanuary 2023, 113HALback to text
 15 inproceedingsRiemannian stochastic optimization methods avoid strict saddle points.Riemannian stochastic optimization methods avoid strict saddle pointsNeurIPS 2023  37th Conference on Neural Information Processing SystemsNew Orleans (LA), United StatesNovember 2023, 127HALback to text
 16 inproceedingsSummarizing taskbased applications behavior over many nodes through progression clustering.PDP 2023  31st Euromicro International Conference on Parallel, Distributed, and NetworkBased ProcessingNaples, ItalyMarch 2023, 18HALback to text
 17 inproceedingsPayoffbased learning with matrix multiplicative weights in quantum games.Proceedings of the 37th International Conference on Neural Information Processing SystemsNeurIPS 2023  37th Conference on Neural Information Processing SystemsNew Orleans (LA), United StatesDecember 2023, 139HALback to text
 18 inproceedingsThe stability of matrix multiplicative weights dynamics in quantum games.Proceedings of the 62nd IEEE Annual Conference on Decision and ControlCDC 2023  62nd IEEE Conference on Decision and ControlSingapore, SingaporeIEEE2023, 18HALback to text
 19 inproceedingsTradingoff price for data quality to achieve fair online allocation.NeurIPS 2023  37th Conference on Neural Information Processing SystemsNew orleans, USA, United StatesDecember 2023HALback to text
 20 inproceedingsExploiting hidden structures in nonconvex games for convergence to Nash equilibrium.Proceedings of the 37th International Conference on Neural Information Processing SystemsNeurIPS 2023  37th Conference on Neural Information Processing SystemsNew Orleans (LA), United States2023, 132HALback to text
 21 inproceedingsA quadratic speedup in finding Nash equilibria of quantum zerosum games.Proceedings of the 2023 Conference on Quantum Techniques in Machine LearningQTML 2023  Annual international conference on Quantum Techniques in Machine LearningCERN, Switzerland2023, 154HALback to text
Doctoral dissertations and habilitation theses
 22 thesisA Modular Approach to Compare Optimization Methods for Bike Sharing Systems.Université Grenoble Alpes [2020....]March 2023HALback to text
 23 phdthesisDecisionMaking in multiagent systems: delays, adaptivity, and learning in games.Université Grenoble AlpesNovember 2023, URL: http://www.theses.fr/s245435back to text
 24 phdthesisMarket design for double auctions.Université Grenoble AlpesMay 2023, URL: http://www.theses.fr/2023GRALM020back to text
 25 thesisAlgorithms for Markovian bandits : Indexability and Learning.Université Grenoble Alpes [2020....]March 2023HALback to text
 26 phdthesisFairness in multistakeholder recommendation platforms.Université Grenoble AlpesJune 2023, URL: http://www.theses.fr/2023GRALM031back to text
 27 phdthesisStrategies for Distributing TaskBased Applications on Heterogeneous Platforms.Université Grenoble AlpesSeptember 2023, URL: http://www.theses.fr/s300803back to text
 28 phdthesisReplica method and asymptotic equivalence.Université Grenoble AlpesDecember 2023, URL: http://www.theses.fr/s252318back to text
 29 phdthesisReinforcement Learning Algorithms for Controlled Queueing Systems.Université Grenoble AlpesDecember 2023, URL: http://www.theses.fr/s276680back to text
Reports & preprints
 30 miscLearning Optimal Admission Control in Partially Observable Queueing Networks.2023HALback to text
 31 miscThe rate of convergence of Bregman proximal methods: Local geometry vs. regularity vs. sharpness.November 2023HALback to text
 32 miscStatistical Discrimination in Stable Matching.April 2023HALback to text
 33 reportA Frenchspeaking training platform for teachers, dedicated to learning computer science, in secondary school..RR9514InriaJune 2023, 15HALback to textback to text
12.2 Cited publications
 34 inproceedingsMeasuring the Facebook Advertising Ecosystem.NDSS 2019  Proceedings of the Network and Distributed System Security SymposiumSan Diego, United StatesFebruary 2019, 115HALDOIback to text
 35 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, 115HALDOIback to text
 36 articleCombining SizeBased Load Balancing with RoundRobin for Scalable Low Latency.IEEE Transactions on Parallel and Distributed Systems2019, 13HALDOIback to textback to text
 37 articleAsymptotically Optimal SizeInterval Task Assignments.IEEE Transactions on Parallel and Distributed Systems30112019, 24222433HALDOIback to textback to text
 38 articlePowerofdChoices with Memory: Fluid Limit and Optimality.Mathematics of Operations Research4532020, 862888HALDOIback to textback to text
 39 inproceedingsDimemas: Predicting MPI Applications Behaviour in Grid Environments.Proc. of the Workshop on Grid Applications and Programming Tools2003back to text
 40 conferencexSim: The ExtremeScale Simulator.HPCSIstanbul, Turkey2011back to text
 41 inproceedingsAutotuning under Tight Budget Constraints: A Transparent Design of Experiments Approach.CCGrid 2019  International Symposium in Cluster, Cloud, and Grid ComputingLarcana, CyprusIEEEMay 2019, 110HALDOIback to text
 42 incollectionComprehensive Performance Tracking with VAMPIR 7.Tools for High Performance Computing 2009The paper details the latest improvements in the Vampir visualization tool.Springer Berlin Heidelberg2010DOIback to text
 43 articlePenaltyRegulated Dynamics and Robust Learning Procedures in Games.Mathematics of Operations Research4032015, 611633HALDOIback to text
 44 articlePerformance analysis methods for listbased caches with nonuniform access.IEEE/ACM Transactions on NetworkingDecember 2020, 118HALDOIback to text
 45 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, 129138HALDOIback to text
 46 inproceedingsFast and Faithful Performance Prediction of MPI Applications: the HPL Case Study.2019 IEEE International Conference on Cluster Computing (CLUSTER)Albuquerque, United StatesSeptember 2019HALDOIback to text
 47 articleSimulationbased Optimization and Sensibility Analysis of MPI Applications: Variability Matters.Journal of Parallel and Distributed ComputingApril 2022HALDOIback to text
 48 articleSimulating MPI applications: the SMPI approach.IEEE Transactions on Parallel and Distributed Systems288August 2017, 14HALDOIback to text
 49 inproceedingsLoad Aware Provisioning of IoT Services on Fog Computing Platform.IEEE International Conference on Communications (ICC)Shanghai, ChinaIEEEMay 2019HALDOIback to text
 50 articleOnline Reconfiguration of IoT Applications in the Fog: The InformationCoordination Tradeoff.IEEE Transactions on Parallel and Distributed Systems3352022, 11561172HALDOIback to text
 51 inproceedings Are meanfield games the limits of finite stochastic games? The 18th Workshop on MAthematical performance Modeling and Analysis Nice, France June 2016 HAL back to text
 52 articleDiscrete Mean Field Games: Existence of Equilibria and Convergence.Journal of Dynamics and Games632019, 119HALDOIback to text
 53 inproceedingsThe Price of Local Fairness in Multistage Selection.IJCAI2019  TwentyEighth International Joint Conference on Artificial IntelligenceMacao, FranceInternational Joint Conferences on Artificial Intelligence OrganizationAugust 2019, 58365842HALDOIback to text
 54 inproceedingsOn Fair Selection in the Presence of Implicit Variance.EC 2020  TwentyFirst ACM Conference on Economics and ComputationBudapest, HungaryACMJuly 2020, 649–675HALDOIback to text
 55 inproceedingsNoregret learning and mixed Nash equilibria: They do not mix.NeurIPS 2020  34th International Conference on Neural Information Processing SystemsVancouver, CanadaDecember 2020, 124HALback to text
 56 articleA Visual Performance Analysis Framework for Taskbased Parallel Applications running on Hybrid Clusters.Concurrency and Computation: Practice and Experience3018April 2018, 131HALDOIback to textback to text
 57 articleSize Expansions of Mean Field Approximation: Transient and SteadyState Analysis.Performance Evaluation2018, 115HALback to text

58
inproceedingsExpected Values Estimated via MeanField Approximation are
$1/N$ Accurate.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, 26HALDOIback to text  59 article Learning algorithms for Markovian Bandits: Is Posterior Sampling more Scalable than Optimism? Transactions on Machine Learning Research Journal November 2022 HAL back to text
 60 unpublishedExponential Convergence Rate for the Asymptotic Optimality of Whittle Index Policy.December 2020, HALback to textback to text
 61 inproceedingsA Refined Mean Field Approximation.ACM SIGMETRICS 2018Irvine, United StatesJune 2018, 1HALback to text
 62 articleLinear Regression from Strategic Data Sources.ACM Transactions on Economics and Computation82May 2020, 124HALDOIback to text
 63 inproceedingsA Refined Mean Field Approximation for Synchronous Population Processes.MAMA 2018Workshop on MAthematical performance Modeling and AnalysisIrvine, United StatesJune 2018, 13HALback to text
 64 inproceedingsAsymptotically Exact TTLApproximations of the Cache Replacement Algorithms LRU(m) and hLRU.28th International Teletraffic Congress (ITC 28)Würzburg, GermanySeptember 2016HALback to text
 65 articleTTL Approximations of the Cache Replacement Algorithms LRU(m) and hLRU.Performance EvaluationSeptember 2017HALDOIback to text
 66 inproceedingsVaccination in a Large Population: Mean Field Equilibrium versus Social Optimum.NETGCOOP 2020  10th International Conference on NETwork Games, COntrol and OPtimizationCargèse, FranceSeptember 2021, 19HALback to text
 67 inproceedingsA Linear Time Algorithm for Computing Offline Speed Schedules Minimizing Energy Consumption.MSR 2019  12ème Colloque sur la Modélisation des Systèmes RéactifsAngers, FranceNovember 2019, 114HALback to text
 68 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, 18HALDOIback to text
 69 articleDynamic Speed Scaling Minimizing Expected Energy Consumption for RealTime Tasks.Journal of SchedulingJuly 2020, 125HALDOIback to text
 70 techreportExploiting Job Variability to Minimize Energy Consumption under RealTime Constraints.RR9300Inria Grenoble RhôneAlpes, Université de Grenoble ; Université Grenoble  AlpesNovember 2019, 23HALback to text
 71 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, 130HALback to text
 72 articleVisualizing the performance of parallel programs.IEEE software85The paper presents Paragraph.1991back to text
 73 inproceedingsPredicting the Energy Consumption of MPI Applications at Scale Using a Single Node.Cluster 2017IEEEHawaii, United StatesSeptember 2017HALback to text
 74 inproceedingsLogGOPSim  Simulating LargeScale Applications in the LogGOPS Model.ACM Workshop on LargeScale System and Application Performance2010back to text
 75 inproceedingsThe limits of minmax optimization algorithms: Convergence to spurious noncritical sets.ICML 2021  38th International Conference on Machine LearningVienna, AustriaJuly 2021HALback to text
 76 articleScaling applications to massively parallel machines using Projections performance analysis tool.Future Generation Comp. Syst.2232006back to text
 77 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, 15HALback to text
 78 articlePerformance Modeling of a Geophysics Application to Accelerate the Tuning of Overdecomposition Parameters through Simulation.Concurrency and Computation: Practice and Experience2018, 121HALDOIback to text
 79 inproceedingsASGriDS: Asynchronous SmartGrids Distributed Simulator.APPEEC 2019  11th IEEE PES AsiaPacific Power and Energy Engineering ConferenceMacao, Macau SAR ChinaIEEEDecember 2019, 15HALback to text
 80 inproceedingsSelection Problems in the Presence of Implicit Bias.Proceedings of the 9th Innovations in Theoretical Computer Science Conference (ITCS)2018, 33:133:17back to text
 81 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, 686695HALDOIback to text
 82 articleThe importance of memory for price discovery in decentralized markets.Games and Economic Behavior125January 2021, 6278HALDOIback to text
 83 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, 14HALback to text
 84 inproceedingsOptimistic Mirror Descent in SaddlePoint Problems: Going the Extra (Gradient) Mile.ICLR 2019  7th International Conference on Learning RepresentationsNew Orleans, United StatesMay 2019, 123HALback to text
 85 inproceedingsQuick or cheap? Breaking points in dynamic markets.EC 2020  21st ACM Conference on Economics and ComputationBudapest, HungaryJuly 2020, 132HALback to text
 86 inproceedingsCycles in adversarial regularized learning.SODA '18  TwentyNinth Annual ACMSIAM Symposium on Discrete AlgorithmsNew Orleans, United StatesJanuary 2018, 27032717HALback to text
 87 articleLearning in games via reinforcement learning and regularization.Mathematics of Operations Research414November 2016, 12971324HALDOIback to textback to text
 88 articleRiemannian game dynamics.Journal of Economic Theory177September 2018, 315364HALDOIback to text
 89 articlePerformance Analysis of Irregular TaskBased Applications on Hybrid Platforms: Structure Matters.Future Generation Computer Systems135October 2022HALback to text
 90 inproceedingsForgetting the Forgotten with Lethe: Conceal Content Deletion from Persistent Observers.PETS 2019  19th Privacy Enhancing Technologies SymposiumStockholm, SwedenJuly 2019, 121HALback to text
 91 articleVAMPIR: Visualization and Analysis of MPI Resources.Supercomputer1211996back to text
 92 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, 110HALDOIback to text
 93 techreportA vaccination policy by zones.Think tank Terra NovaOctober 2020HALback to text
 94 articleSARSCoV2 elimination, not mitigation, creates best outcomes for health, the economy, and civil liberties.The Lancet39710291June 2021, 22342236HALDOIback to text
 95 inproceedingsGreen bridges: Reconnecting Europe to avoid economic disaster.Europe in the Time of Covid192020HALback to text
 96 inproceedingsPARAVER: A tool to visualise and analyze parallel code.Proceedings of Transputer and Occam Developments, WOTUG18.441995back to text
 97 articleMarket sentiments and convergence dynamics in decentralized assignment economies.International Journal of Game Theory491March 2020, 275298HALDOIback to text
 98 techreportFocus mass testing: How to overcome low test accuracy.Esade Centre for Economic PolicyDecember 2020HALback to text
 99 articleGreen zoning: An effective policy tool to tackle the Covid19 pandemic.Health Policy1258August 2021, 981986HALDOIback to text
 100 inproceedingsScalable performance analysis: the Pablo performance analysis environment.Scalable Parallel Libraries Conference1993back to text
 101 thesisToward transparent and parsimonious methods for automatic performance tuning.UGA (Université Grenoble Alpes); USP (Universidade de São Paulo)July 2021HALback to text
 102 inproceedingsThe eyes have it: A task by data type taxonomy for information visualizations.IEEE Symposium on Visual LanguagesIEEE1996back to text
 103 inproceedingsPower Management and Dynamic Voltage Scaling: Myths and Facts.Proceedings of the 2005 Workshop on Power Aware Realtime ComputingNew Jersey, USASeptember 2005back to text
 104 inproceedingsPotential for Discrimination in Online Targeted Advertising.FAT 2018  Conference on Fairness, Accountability, and Transparency81NewYork, United StatesFebruary 2018, 115HALback to text
 105 inproceedingsPSINS: An Open Source Event Tracer and Execution Simulator for MPI Applications.EuroPar2009back to text
 106 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 States2018HALback to text
 107 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, 13HALback to text
 108 inproceedingsDecentralized Optimization of Energy Exchanges in an Electricity Microgrid .ACM eEnergy 2016  7th ACM International Conference on Future Energy SystemsWaterloo, CanadaJune 2016HALDOIback to text
 109 inproceedingsDecentralized optimization of energy exchanges in an electricity microgrid.2016 IEEE PES Innovative Smart Grid Technologies Conference Europe (ISGTEurope)Ljubljana, SloveniaIEEEOctober 2016, 16HALDOIback to text
 110 articleOn an Index Policy for Restless Bandits.Journal of Applied Probability2731990, 637648URL: http://www.jstor.org/stable/3214547back to text
 111 inproceedingsScheduling for Reduced CPU Energy.Proceedings of the 1st USENIX Conference on Operating Systems Design and ImplementationOSDI '94USAMonterey, CaliforniaUSENIX Association1994, 2–esback to text
 112 inproceedingsValidation and Uncertainty Assessment of ExtremeScale HPC Simulation through Bayesian Inference.EuroPar2013back to text
 113 articleToward Scalable Performance Visualization with Jumpshot.International Journal of High Performance Computing Applications1331999DOIback to text
 114 inproceedingsBigSim: A Parallel Simulator for Performance Prediction of Extremely Large Parallel Machines.IPDPS2004back to text
 115 articleImproving the Performance of Batch Schedulers Using Online Job Runtime Classification.Journal of Parallel and Distributed Computing164February 2022, 8395HALDOIback to text