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 low-cost and energy-efficient 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 ever-growing size, intrinsic heterogeneity and distributedness, user-driven 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, open-loop 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, spatio-temporal 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 game-theoretic 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 (Multi-armed bandits, Q-learning, 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);
• Multi-agent 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 (mean-field 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 multi-agent 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 able of doing so quickly (low regret), even when facing the difficulties associated to a distributed context (lack of coordination, uncertain world, information delay, limited feedback, …)

In the rest of this document, we describe in detail our new results in the above areas.

3.1 Performance Evaluation

Participants: Jonatha Anselmi, Vincent Danjean, Nicolas Gast, Guillaume Huard, Arnaud Legrand, Florence Perronnin, Jean-Marc Vincent.

3.2 Asymptotic Methods

Participants: Jonatha Anselmi, Romain Couillet, Nicolas Gast, Bruno Gaujal, Florence Perronnin, Jean-Marc Vincent.

3.3 Distributed Online Optimization and Learning in Games

Participants: Nicolas Gast, Romain Couillet, Bruno Gaujal, Arnaud Legrand, Patrick Loiseau, Panayotis Mertikopoulos, Bary Pradelski.

3.4 Responsible Computer Science

Participants: Nicolas Gast, Romain Couillet, Bruno Gaujal, Arnaud Legrand, Patrick Loiseau, Panayotis Mertikopoulos, Bary Pradelski.

4.1 Large Computing Infrastructures

Supercomputers typically comprise thousands to millions of multi-core 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 Next-Generation Wireless Networks

Considerable interest has arisen from the seminal prediction that the use of multiple-input, multiple-output (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 re-regulation) 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, small-cell environments – the continued transition to fifth generation (5G) wireless networks is expected to go hand-in-hand with distributed learning and optimization methods that can operate reliably in feedback-starved environments. Accordingly, one of POLARIS' application-driven goals will be to leverage the algorithmic output of Theme 5 into a highly adaptive resource allocation framework for next-géneration 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 mean-field approximation to build decentralized algorithms that solve complex optimization problems. We focus on two problems: decentralized control of electric grids and capacity planning in vehicle-sharing 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.

5.1 Footprint of research activities

The carbon footprint of the team has been quite minimal in 2021 since there has been no travel allowed with most of us working from home. Our team does not train heavy ML models requiring important processing power although some of us perform computer science experiments, mostly using the Grid5000 platforms. We keep this usage very reasonable and rely on cheaper alternatives (e.g., simulations) as much as possible.

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 Grenoble-INP, as well as to associations in Grenoble (FNE, AgirAlternatif). He is also co-responsible of the Digital Transformation DU. He has published three articles on the issue of "usability" of artificial intelligence, and is the organizer of a special session on "Signal processing and resilience" for the GRETSI 2022 conference. He is also co-creator 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. See section 11.2 and 11.3.3 for more details.

5.3 Impact of research results

The efforts of Barry Pradelski on COVID policy have received lots of media coverage and he was appointed to share his expertise to the Centre européen de prévention et de contrôle des maladies (ECDC).

Jean-Marc Vincent is heavily engaged since several years in the training of computer science teachers at the elementary/middle/high school levels 47. 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 and 11.3.3 for more details.

6.1 Awards

• The paper "Energy optimal activation of processors for the execution of a single task with unknown size" 17, authored by J. Anselmi and B. Gaujal, won the best paper award at the international conference IEEE MASCOTS 2022.
• The paper "Robust power management via learning and game design"  124, by Z. Zhou, P. Mertikopoulos, A. L. Moustakas, N. Bambos, and P. W. Glynn, published in Operations Research, 69(1):331–345, in January 2021 won the INFORMS best paper award in the network analytics section.
• The paper "UnderGrad: A universal black-box optimization method with almost dimension-free convergence rate guarantees" 19, authored by K. Antonakopoulos, D. Q. Vu, V. Cevher, K. Levy, and P. Mertikopoulos, won the best paper award at the ICML'22 conference.
• Panayotis Mertikopoulos was recognized as an Outstanding reviewer at ICLR 2022.
• The book "Random matrix methods for machine learning" 35 by R. Couillet and Z. Liao has been published at Cambridge University Press in June 2022.

7.1 New software

8.1 Performance evaluation of large systems

Participants: Sebastian Allmeier, Vincent Danjean, Arnaud Legrand, Nicolas Gast, Guillaume Huard, Jean-Marc Vincent.

Finely tuning applications and understanding the influence of key parameters (number of processes, granularity, collective operation algorithms, virtual topology, and process placement) is critical to obtain good performance on supercomputers. With the high consumption of running applications at scale, doing so solely to optimize their performance is particularly costly. We have shown in 3 that SimGrid and SMPI simgrid.org could be used to obtain inexpensive but faithful predictions of expected performance. The methodology we propose decouples the complexity of the platform, which is captured through statistical models of the performance of its main components (MPI communications, BLAS operations), from the complexity of adaptive applications by emulating the application and skipping regular non-MPI parts of the code. We demonstrate the capability of our method with High-Performance Linpack (HPL), the benchmark used to rank supercomputers in the TOP500, which requires careful tuning. This work presents an extensive (in)validation study that compares simulation with real experiments and demonstrates our ability to predict the performance of HPL within a few percent consistently. This study allows us to identify the main modeling pitfalls (e.g., spatial and temporal node variability or network heterogeneity and irregular behavior) that need to be considered. Our “surrogate” also allows studying several subtle HPL parameter optimization problems while accounting for uncertainty on the platform.

We have also shown in 13 how the structure of complex applications such as a multifrontal sparse linear solvers could be exploited to detect and correct non-trivial performance problems. Efficiently exploiting computational resources in heterogeneous platforms is a real challenge which has motivated the adoption of the task-based programming paradigm where resource usage is dynamic and adaptive. Unfortunately, classical performance visualization techniques used in routine performance analysis often fail to provide any insight in this new context, especially when the application structure is irregular. We propose and implement in StarVZ several performance visualization techniques tailored for the analysis of task-based multifrontal sparse linear solvers and show that by building on both a performance model of irregular tasks and on structure of the application (in particular the elimination tree), we can detect and highlight anomalies and understand resource utilization from the application point-of-view in a very insightful way. We validate these novel performance analysis techniques with the QR_mumps sparse parallel solver by describing a series of case studies where we identify and address non trivial performance issues thanks to our visualization methodology.

Large systems can be particularly difficult to analyze because of inherent state-space explosion and most computations become untractable. Mean field approximation is a powerful technique to study the performance of very large stochastic systems represented as systems of interacting objects. Applications include load balancing models, epidemic spreading, cache replacement policies, or large-scale data centers, for which mean field approximation gives very accurate estimates of the transient or steady-state behaviors. In a series of recent papers, a new and more accurate approximation, called the refined mean field approximation has been presented. A key strength of this technique lies in its applicability to not-so-large systems. Yet, computing this new approximation can be cumbersome, which is why develop a tool, called rmf tool and available at github.com/ngast/rmf_tool, that takes the description of a mean field model, and can numerically compute its mean field approximations and refinement.

Mean field approximation is asymptotically exact for systems composed of $n$ homogeneous objects under mild conditions. In  1, we study what happens when objects are heterogeneous. This can represent servers with different speeds or contents with different popularities. We define an interaction model that allows obtaining asymptotic convergence results for stochastic systems with heterogeneous object behavior, and show that the error of the mean field approximation is of order $O(1/n)$. More importantly, we show how to adapt the refined mean field approximation and show that the error of this approximation is reduced to $O(1/n^2)$. To illustrate the applicability of our result, we present two examples. The first addresses a list-based cache replacement model, $RANDOM\left(m\right)$, which is an extension of the $RANDOM$ policy. The second is a heterogeneous supermarket model. These examples show that the proposed approximations are computationally tractable and very accurate. They also show that for moderate system sizes (30) the refined mean field approximation tends to be more accurate than simulations for any reasonable simulation time.

8.2 Energy optimization

Participants: Jonatha Anselmi, Bruno Gaujal, Louis-Sébastien Rebuffi.

A key objective in the management of modern computer systems consists in minimizing the electrical energy consumed by processing resources while satisfying certain target performance criteria. In 17, we consider the execution of a single task with unknown size on top of a service system that offers a limited number of processing speeds, say $N$, and investigate the problem of finding a speed profile that minimizes the resulting energy consumption subject to a deadline constraint. Existing works mainly investigated this problem when speed profiles are continuous functions. In contrast, the novelty of our work is to consider discontinuous speed profiles, i.e., a case that arises naturally when the underlying computational platform offers a finite number of speeds. In our main result, we show that the computation of an optimal speed profile boils down to solving a convex optimization problem. Under mild assumptions, for such convex optimization we prove some structural results that yield the formulation of an extremely efficient solution algorithm. Specifically, we show that the optimal speed profile can be computed by solving $O(logN)$ one-dimensional equations. Our results hold when the task size follows a known probability distribution function and the set of available speeds, if listed in increasing order, forms a sublinear concave sequence.

More generally, energy optimization should be performed at a global scale and requires to revisit load balancing strategies. Techniques like replication and speculation are double-edged weapons that must be handled with caution as the resource overhead may be detrimental when used too aggressively. We have studied such strategies in previous work and presented an overview 2 in the special issue of Queueing Systems, 100 views on queues.

8.3 Large system performance optimization through learning techniques

Participants: Arnaud Legrand, Lucas Leandro Nesi, Panayotis Mertikopoulos.

Large infrastructures and computing applications typically exhibit some form of regularity which should be exploited but their stochastic nature makes their optimization difficult. In this series of work, we demonstrate that simple machine and reinforcement learning techniques can be tailored to optimize these systems.

Parallel applications performance strongly depends on the number of resources. Although adding new nodes usually reduces execution time, excessive amounts are often detrimental as they incur substantial communication overhead, which is difficult to anticipate. Characteristics like network contention, data distribution methods, synchronizations, and how communications and computations overlap generally impact the performance. Finding the correct number of resources can thus be particularly tricky for multi-phase applications as each phase may have very different needs, and the popularization of hybrid (CPU+GPU) machines and heterogeneous partitions makes it even more difficult. In  32, we study and propose, in the context of a task-based GeoStatistic application, strategies for the application to actively learn and adapt to the best set of heterogeneous nodes it has access to. We propose strategies that use the Gaussian Process method with trends, bound mechanisms for reducing the search space, and heterogeneous behavior modeling. We compare these methods with traditional exploration strategies in 16 different machines scenarios. In the end, the proposed strategies are able to gain up to $\approx 51\%$ compared to the standard case of using all the nodes while having low overhead.

At the scale of the whole high-performance computing platform, job scheduling is also a hard problem that involves uncertainties on both the job arrival process and their execution times. Users typically provide only loose upper bounds for job execution times, which are not so useful for scheduling heuristics based on processing times. Previous studies focused on applying regression techniques to obtain better execution time estimates, which worked reasonably well and improved scheduling metrics. However, these approaches require a long period of training data. In 16, we propose a simpler approach by classifying jobs as small or large and prioritizing the execution of small jobs over large ones. Indeed, small jobs are the most impacted by queuing delays, but they typically represent a light load and incur a small burden on the other jobs. The classifier operates online and learns by using data collected over the previous weeks, facilitating its deployment and enabling a fast adaptation to changes in the workload characteristics. We evaluate our approach using four scheduling policies on seven HPC platform workload traces. We show that: first, incorporating such classification reduces the average bounded slowdown of jobs in all scenarios, second, in most considered scenarios, the improvements are comparable to the ideal hypothetical situation where the scheduler would know in advance the exact running time of jobs.

In 4, we evaluate the relevance of bandit-like strategies for the Fog computing context and explore the information-coordination trade-off. Fog computing emerges as a potential solution to handle the growth of traffic and processing demands, providing nearby resources to run IoT applications. In this paper, we consider the reconfiguration problem, i.e., how to dynamically adapt the placement of IoT applications running in the Fog, depending on application needs and evolution of resource usage. We propose and evaluate a series of reconfiguration algorithms, based on both online scheduling (dynamic packing) and online learning (bandit) approaches. Through an extensive set of experiments in a realistic testbed built on Grid5000 and FIT-IoT lab, we demonstrate that the performance strongly and mainly depends on the quality and availability of information from both Fog infrastructure and IoT applications. We show that a reactive and greedy strategy can overcome the performance of state-of-the-art online learning algorithms, as long as the strategy has access to a little extra information.

Finally, the high degree of variability present in current and emerging mobile wireless networks calls for mathematical tools and techniques that transcend classical (convex) optimization paradigms. In 20, we provide a gentle introduction to online learning and optimization algorithms that are able to provably cope with this variability and provide policies that are asymptotically optimal in hindsight-a property known as no regret. The focal point of this survey is to delineate the trade-off between the information available as feedback to the learner, and the achievable regret guarantees starting with the case of gradient-based (first-order) feedback, then moving on to value-based (zeroth-order) feedback, and, ultimately, pushing the envelope to the extreme case of a single bit of feedback. We illustrate our theoretical analysis with a series of practical wireless network examples that highlight the potential of this elegant toolbox.

8.4 Exploiting specific structures in reinforcement learning

Participants: Jonatha Anselmi, Yan Chen, Kimang Khun, Nicolas Gast, Bruno Gaujal, Louis-Sébastin Rebuffi, Panayotis Mertikopoulos.

The Multi-armed Stochastic Bandit framework is a classic reinforcement learning problem to study the exploration exploitation trade-off dilemma and for which several optimal algorithms like UCB 2 and Thompson sampling3, whose optimality has only recently been proved by Kaufmann et al.4, have been proposed. Although the first strategy is an optimistic strategy which systematically chooses the "most promising" arm, the second one build on a Bayesian perspective and samples the posterior to decide which arm to select. The Markovian Bandit allows to model situations where the reward distribution is modeled as a Markov chain and may thus exhibit temporal changes. A key challenge in this context is the curse of dimensionality, which basically says that the state size of the Markov process is exponential in the number of the system components so that the complexity of computing an optimal policy and its value are exponential. This is why specific algorithms should be designed to exploit the very specific structures that some state space exhibit. Based on earlier results, we have presented these lines of thought in two articles in special issue of Queueing Systems, 100 views on queues: Learning in Queues7, and Why (and When) do Asymptotic Methods Work so well?6.

Restless bandits are a specific kind of bandits in which the state of each arm evolves according to a Markov process independently of the learner's actions. Most restless Markovian bandits problems in infinite horizon can be solved quasioptimally using the famous Whittle index, which is a generalization of the Gittins index. In 41, we develop an algorithm to test the indexability and compute the Whittle indices of any finite-state restless bandit arm. This algorithm works in the discounted and non-discounted 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 (k - 1)-th smallest, and to test indexability, (2) the use of the Sherman-Morrison 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 Sherman-Morrison formula leads to an algorithm that computes Whittle index in $2/3n^3+o\left(n^3\right)$ 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.

In 42, we 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 LP-index policy that is asymptotically optimal with square root convergence rate on all models, and with exponential rate if the model is non-degenerate in finite horizon, and satisfies a uniform global attractor property in infinite horizon. We next define the LP-update policy, which is essentially a repeated LP-index policy that solves a new linear program at each decision epoch. We provide numerical experiments to compare the efficiency of LP-based policies. We compare the performance of the LP-index policy and the LP-update policy with other heuristics. Our result demonstrates that the LP-update policy outperforms the LP-index policy in general, and can have a significant advantage when the transition matrices are wrongly estimated.

In 33, we revisit the regret of undiscounted reinforcement learning in MDPs with a birth and death structure, which are typical of queuing systems. Specifically, we consider a controlled queue with impatient jobs and the main objective is to optimize a trade-off between energy consumption and user-perceived performance. Within this setting, the diameter $D$ of the MDP is $\Omega \left(S^S\right)$, where $S$ is the number of states. Therefore, the existing lower and upper bounds on the regret at time $T$, of order $O\left(\sqrt{DSAT}\right)$ for MDPs with $S$ states and $A$ actions, may suggest that reinforcement learning is inefficient here. In our main result however, we exploit the structure of our MDPs to show that the regret of a slightly-tweaked version of the classical learning algorithm UCRL2 is in fact upper bounded by $\widetilde{𝒪}\left(\sqrt{E_{2}AT}\right)$ where $E_2$ is related to the weighted second moment of the stationary measure of a reference policy. Importantly, $E_2$ is bounded independently of S. Thus, our bound is asymptotically independent of the number of states and of the diameter. This result is based on a careful study of the number of visits performed by the learning algorithm to the states of the MDP, which is highly non-uniform.

Finally, in many online decision processes, the optimizing agent is called to choose between large numbers of alternatives with many inherent similarities; in turn, these similarities imply closely correlated losses that may confound standard discrete choice models and bandit algorithms. We study this question in the context of nested bandits, a class of adversarial multi-armed bandit problems where the learner seeks to minimize their regret in the presence of a large number of distinct alternatives with a hierarchy of embedded (non-combinatorial) similarities. In this setting, optimal algorithms based on the exponential weights blueprint (like Hedge, EXP3, and their variants) may incur significant regret because they tend to spend excessive amounts of time exploring irrelevant alternatives with similar, suboptimal costs. To account for this, we propose in 30 a nested exponential weights (NEW) algorithm that performs a layered exploration of the learner's set of alternatives based on a nested, step-by-step selection method. In so doing, we obtain a series of tight bounds for the learner's regret showing that online learning problems with a high degree of similarity between alternatives can be resolved efficiently, without a red bus / blue bus paradox occurring.

8.5 Distributed learning and optimization

Participants: Yu-Guan Hsieh, Panayotis Mertikopoulos.

Many learning algorithms operate in centralized way, which raises many practical issues in terms of scalability, privacy, hence a high interest for designing efficient distributed and federated machine learning algorithms. In such context it is essential to design systems that can seamlessly adapt to the workload and to the evolving behaviour of its components (users, resources, network).

In 43 we consider decentralized optimization problems in which a number of agents collaborate to minimize the average of their local functions by exchanging over an underlying communication graph. Specifically, we place ourselves in an asynchronous model where only a random portion of nodes perform computation at each iteration, while the information exchange can be conducted between all the nodes and in an asymmetric fashion. For this setting, we propose an algorithm that combines gradient tracking and variance reduction over the entire network. This enables each node to track the average of the gradients of the objective functions. Our theoretical analysis shows that the algorithm converges linearly, when the local objective functions are strongly convex, under mild connectivity conditions on the expected mixing matrices. In particular, our result does not require the mixing matrices to be doubly stochastic. In the experiments, we investigate a broadcast mechanism that transmits information from computing nodes to their neighbors, and confirm the linear convergence of our method on both synthetic and real-world datasets.

One of the most widely used methods for solving large-scale stochastic optimization problems is distributed asynchronous stochastic gradient descent (DASGD), a family of algorithms that result from parallelizing stochastic gradient descent on distributed computing architectures (possibly) asychronously. However, a key obstacle in the efficient implementation of DASGD is the issue of delays: when a computing node contributes a gradient update, the global model parameter may have already been updated by other nodes several times over, thereby rendering this gradient information stale. These delays can quickly add up if the computational throughput of a node is saturated, so the convergence of DASGD may be compromised in the presence of large delays. In 15, we show that, by carefully tuning the algorithm's step-size, convergence to the critical set is still achieved in mean square, even if the delays grow unbounded at a polynomial rate. We also establish finer results in a broad class of structured optimization problems (called variationally coherent), where we show that DASGD converges to a global optimum with probability 1 under the same delay assumptions. Together, these results contribute to the broad landscape of large-scale non-convex stochastic optimization by offering state-of-the-art theoretical guarantees and providing insights for algorithm design.

In 10, we provide a general framework for studying multi-agent online learning problems in the presence of delays and asynchronicities. Specifically, we propose and analyze a class of adaptive dual averaging schemes in which agents only need to accumulate gradient feedback received from the whole system, without requiring any between-agent coordination. In the single-agent case, the adaptivity of the proposed method allows us to extend a range of existing results to problems with potentially unbounded delays between playing an action and receiving the corresponding feedback. In the multi-agent case, the situation is significantly more complicated because agents may not have access to a global clock to use as a reference point; to overcome this, we focus on the information that is available for producing each prediction rather than the actual delay associated with each feedback. This allows us to derive adaptive learning strategies with optimal regret bounds, even in a fully decentralized, asynchronous environment. Finally, we also analyze an "optimistic" variant of the proposed algorithm which is capable of exploiting the predictability of problems with a slower variation and leads to improved regret bounds.

In decentralized optimization environments, each agent $i$ in a network of $n$ nodes has its own private function $f_i$, and nodes communicate with their neighbors to cooperatively minimize the aggregate objective ${\sum }_{i=1}^n{f}_i$. In this setting, synchronizing the nodes' updates incurs significant communication overhead and computational costs, so much of the recent literature has focused on the analysis and design of asynchronous optimization algorithms, where agents activate and communicate at arbitrary times without needing a global synchronization enforcer. However, most works assume that when a node activates, it selects the neighbor to contact based on a fixed probability (e.g., uniformly at random), a choice that ignores the optimization landscape at the moment of activation. Instead, in 21 we introduce an optimization-aware selection rule that chooses the neighbor providing the highest dual cost improvement (a quantity related to a dualization of the problem based on consensus). This scheme is related to the coordinate descent (CD) method with the Gauss-Southwell (GS) rule for coordinate updates; in our setting however, only a subset of coordinates is accessible at each iteration (because each node can communicate only with its neighbors), so the existing literature on GS methods does not apply. To overcome this difficulty, we develop a new analytical framework for smooth and strongly convex $f_i$ that covers the class of set-wise CD algorithms – a class that directly applies to decentralized scenarios, but is not limited to them – and we show that the proposed setwise GS rule achieves a speedup factor of up to the maximum degree in the network (which is in the order of $\Theta \left(n\right)$ for highly connected graphs). The speedup predicted by our analysis is validated in numerical experiments with synthetic data.

8.6 Learning in games

Participants: Kimon Antonakopoulos, Yu Guan Hsieh, Panayotis Mertikopoulos, Bary Pradelski, Patrick Loiseau.

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.

In 24, we examine the problem of regret minimization when the learner is involved in a continuous game with other optimizing agents: in this case, if all players follow a no-regret algorithm, it is possible to achieve significantly lower regret relative to fully adversarial environments. We study this problem in the context of variationally stable games (a class of continuous games which includes all convex-concave and monotone games), and when the players only have access to noisy estimates of their individual payoff gradients. If the noise is additive, the game-theoretic and purely adversarial settings enjoy similar regret guarantees; however, if the noise is multiplicative, we show that the learners can, in fact, achieve constant regret. We achieve this faster rate via an optimistic gradient scheme with learning rate separation that is, the method's extrapolation and update steps are tuned to different schedules, depending on the noise profile. Subsequently, to eliminate the need for delicate hyperparameter tuning, we propose a fully adaptive method that smoothly interpolates between worst-and best-case regret guarantees.

In 9, we examine the long-run behavior of a wide range of dynamics for learning in nonatomic games, in both discrete and continuous time. The class of dynamics under consideration includes fictitious play and its regularized variants, the best reply dynamics (again, possibly regularized), as well as the dynamics of dual averaging / "follow the regularized leader" (which themselves include as special cases the replicator dynamics and Friedman's projection dynamics). Our analysis concerns both the actual trajectory of play and its time-average, and we cover potential and monotone games, as well as games with an evolutionarily stable state (global or otherwise). We focus exclusively on games with finite action spaces; nonatomic games with continuous action spaces are treated in detail in Part II of this work.

In 45, we develop a unified stochastic approximation framework for analyzing the long-run behavior of multi-agent online learning in games. Our framework is based on a "primal-dual", mirrored Robbins-Monro (MRM) template which encompasses a wide array of popular game-theoretic learning algorithms (gradient methods, their optimistic variants, the EXP3 algorithm for learning with payoff-based feedback in finite games, etc.). In addition to providing an integrated view of these algorithms, the proposed MRM blueprint allows us to obtain a broad range of new convergence results, both asymptotic and in finite time, in both continuous and finite games.

Learning in stochastic games is a notoriously difficult problem because, in addition to each other's strategic decisions, the players must also contend with the fact that the game itself evolves over time, possibly in a very complicated manner. Because of this, the convergence properties of popular learning algorithms - like policy gradient and its variants - are poorly understood, except in specific classes of games (such as potential or two-player, zero-sum games). In view of this, we examine in 23 the long-run behavior of policy gradient methods with respect to Nash equilibrium policies that are second-order stationary (SOS) in a sense similar to the type of sufficiency conditions used in optimization. Our first result is that SOS policies are locally attracting with high probability, and we show that policy gradient trajectories with gradient estimates provided by the REINFORCE algorithm achieve an $O(1/\sqrt{n})$ distance-squared convergence rate if the method's step-size is chosen appropriately. Subsequently, specializing to the class of deterministic Nash policies, we show that this rate can be improved dramatically and, in fact, policy gradient methods converge within a finite number of iterations in that case.

In 5, we examine the long-run behavior of multi-agent 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 time-varying 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 gradient-based and payoff-based feedback - i.e., when players only get to observe the payoffs of their chosen actions.

In 29, we also investigate the impact of feedback quantization on multi-agent learning. In particular, we analyze the equilibrium convergence properties of the well-known "follow the regularized leader" (FTRL) class of algorithms when players can only observe a quantized (and possibly noisy) version of their payoffs. In this information-constrained setting, we show that coarser quantization triggers a qualitative shift in the convergence behavior of FTRL schemes. Specifically, if the quantization error lies below a threshold value (which depends only on the underlying game and not on the level of uncertainty entering the process or the specific FTRL variant under study), then (i) FTRL is attracted to the game's strict Nash equilibria with arbitrarily high probability; and (ii) the algorithm's asymptotic rate of convergence remains the same as in the non-quantized case. Otherwise, for larger quantization levels, these convergence properties are lost altogether: players may fail to learn anything beyond their initial state, even with full information on their payoff vectors. This is in contrast to the impact of quantization in continuous optimization problems, where the quality of the obtained solution degrades smoothly with the quantization level.

Finally, the literature on evolutionary game theory suggests that pure strategies that are strictly dominated by other pure strategies always become extinct under imitative game dynamics, but they can survive under innovative dynamics. As we explain in 12, this is because innovative dynamics favour rare strategies while standard imitative dynamics do not. However, as we also show, there are reasonable imitation protocols that favour rare or frequent strategies, thus allowing strictly dominated strategies to survive in large classes of imitation dynamics. Dominated strategies can persist at nontrivial frequencies even when the level of domination is not small.

8.7 Advanced learning and optimization methods

Participants: Kimon Antonakopoulos, Yu Guan 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.

In 39, we examine the last-iterate convergence rate of Bregman proximal methods - from mirror descent to mirror-prox - in constrained variational inequalities. Our analysis shows that the convergence speed of a given method depends sharply on the Legendre exponent of the underlying Bregman regularizer (Euclidean, entropic, or other), a notion that measures the growth rate of said regularizer near a solution. In particular, we show that boundary solutions exhibit a clear separation of regimes between methods with a zero and non-zero Legendre exponent respectively, with linear convergence for the former versus sublinear for the latter. This dichotomy becomes even more pronounced in linearly constrained problems where, specifically, Euclidean methods converge along sharp directions in a finite number of steps, compared to a linear rate for entropic methods.

Universal methods for optimization are designed to achieve theoretically optimal convergence rates without any prior knowledge of the problem's regularity parameters or the accuracy of the gradient oracle employed by the optimizer. In this regard, existing state-of-the-art algorithms achieve an $O(1/T^2)$ value convergence rate in Lipschitz smooth problems with a perfect gradient oracle, and an $O(1/\sqrt{T})$ convergence rate when the underlying problem is non-smooth and/or the gradient oracle is stochastic. On the downside, these methods do not take into account the problem's dimensionality, and this can have a catastrophic impact on the achieved convergence rate, in both theory and practice. In 19 we aim to bridge this gap by providing a scalable universal gradient method - dubbed UnderGrad - whose oracle complexity is almost dimension-free in problems with a favorable geometry (like the simplex, linearly constrained semidefinite programs and combinatorial bandits), while retaining the order-optimal dependence on $T$ described above. These "best-of-both-worlds" results are achieved via a primal-dual update scheme inspired by the dual exploration method for variational inequalities.

Adaptive first-order methods in optimization are prominent in machine learning and data science owing to their ability to automatically adapt to the landscape of the function being optimized. However, their convergence guarantees are typically stated in terms of vanishing gradient norms, which leaves open the issue of converging to undesirable saddle points (or even local maximizers). In 18, we focus on the AdaGrad family of algorithms-with scalar, diagonal or full-matrix preconditioning-and we examine the question of whether the method's trajectories avoid saddle points. A major challenge that arises here is that AdaGrad's step-size (or, more accurately, the method's preconditioner) evolves over time in a filtration-dependent way, i.e., as a function of all gradients observed in earlier iterations; as a result, avoidance results for methods with a constant or vanishing step-size do not apply. We resolve this challenge by combining a series of step-size stabilization arguments with a recursive representation of the AdaGrad preconditioner that allows us to employ stable manifold techniques and ultimately show that the induced trajectories avoid saddle points from almost any initial condition.

Many important learning algorithms, such as stochastic gradient methods, are often deployed to solve nonlinear problems on Riemannian manifolds. Motivated by these applications, we propose in 25 a family of Riemannian algorithms generalizing and extending the seminal stochastic approximation framework of Robbins and Monro. Compared to their Euclidean counterparts, Riemannian iterative algorithms are much less understood due to the lack of a global linear structure on the manifold. We overcome this difficulty by introducing an extended Fermi coordinate frame which allows us to map the asymptotic behavior of the proposed Riemannian Robbins-Monro (RRM) class of algorithms to that of an associated deterministic dynamical system under very mild assumptions on the underlying manifold. In so doing, we provide a general template of almost sure convergence results that mirrors and extends the existing theory for Euclidean Robbins-Monro schemes, albeit with a significantly more involved analysis that requires a number of new geometric ingredients. We showcase the flexibility of the proposed RRM framework by using it to establish the convergence of a retraction-based analogue of the popular optimistic / extra-gradient methods for solving minimization problems and games, and we provide a unified treatment for their convergence.

Last, in 44, we propose and analyze exact and inexact regularized Newton-type methods for finding a global saddle point of a convex-concave unconstrained min-max optimization problem. Compared to their first-order counterparts, investigations of second-order methods for min-max optimization are relatively limited, as obtaining global rates of convergence with second-order information is much more involved. In this paper, we highlight how second-order information can be used to speed up the dynamics of dual extrapolation methods despite inexactness. Specifically, we show that the proposed algorithms generate iterates that remain within a bounded set and the averaged iterates converge to an $ϵ$-saddle point within $O\left({ϵ}^{-2/3}\right)$ iterations in terms of a gap function. Our algorithms match the theoretically established lower bound in this context and our analysis provides a simple and intuitive convergence analysis for second-order methods without requiring any compactness assumptions. Finally, we present a series of numerical experiments on synthetic and real data that demonstrate the efficiency of the proposed algorithms.

8.8 Random matrix analysis and Machine Learning

Participants: Romain Couillet, Hugo Lebeau.

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.

Several machine learning problems such as latent variable model learning and community detection can be addressed by estimating a low-rank signal from a noisy tensor. Despite recent substantial progress on the fundamental limits of the corresponding estimators in the large-dimensional setting, some of the most significant results are based on spin glass theory, which is not easily accessible to non-experts. In 8, we propose a sharply distinct and more elementary approach, relying on tools from random matrix theory. The key idea is to study random matrices arising from contractions of a random tensor, which give access to its spectral properties. In particular, for a symmetric $d$-th order rank-one model with Gaussian noise, our approach yields a novel characterization of maximum likelihood (ML) estimation performance in terms of a fixed-point equation valid in the regime where weak recovery is possible. For $d=3$, the solution to this equation matches the existing results. We conjecture that the same holds for any order $d$, based on numerical evidence for $d\in 4,5$. Moreover, our analysis illuminates certain properties of the large-dimensional ML landscape. Our approach can be extended to other models, including asymmetric and non-Gaussian ones.

In 11, we introduce a random matrix framework for the analysis of clustering on high-dimensional data streams, a particularly relevant setting for a more sober processing of large amounts of data with limited memory and energy resources. Assuming data $x_1,x_2,...$ arrives as a continuous flow and a small number $L$ of them can be kept in the learning pipeline, one has only access to the diagonal elements of the Gram kernel matrix: ${\left[K_L\right]}_{i,j}=\frac{1}{p}{x}_i^T{x}_j{1}_{|i-j|<L}$. Under a large-dimensional data regime, we derive the limiting spectral distribution of the banded kernel matrix $K_L$ and study its isolated eigenvalues and eigenvectors, which behave in an unfamiliar way. We detail how these results can be used to perform efficient online kernel spectral clustering and provide theoretical performance guarantees. Our findings are empirically confirmed on image clustering tasks. Leveraging on optimality results of spectral methods for clustering, this work offers insights on efficient online clustering techniques for high-dimensional data. This work has also been presented at the GRETSI 28.

8.9 Fairness and equity in digital (recommendation, advertising, persistent storage) systems

Participants: Nicolas Gast, Patrick Loiseau, Rémi Molina, Bary Pradelski, Benjamin Roussillon, Till Kletti.

The general deployment of machine-learning 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.

Discrimination in machine learning often arises along multiple dimensions (a.k.a. protected attributes); it is then desirable to ensure intersectional fairness-i.e., that no subgroup is discriminated against. It is known that ensuring marginal fairness for every dimension independently is not sufficient in general. Due to the exponential number of subgroups, however, directly measuring intersectional fairness from data is impossible. In 31, our primary goal is to understand in detail the relationship between marginal and intersectional fairness through statistical analysis. We first identify a set of sufficient conditions under which an exact relationship can be obtained. Then, we prove bounds (easily computable through marginal fairness and other meaningful statistical quantities) in high probability on intersectional fairness in the general case. Beyond their descriptive value, we show that these theoretical bounds can be leveraged to derive a heuristic improving the approximation and bounds of intersectional fairness by choosing, in a relevant manner, protected attributes for which we describe intersectional subgroups. Finally, we test the performance of our approximations and bounds on real and synthetic data-sets.

To better understand discriminations and the effect of affirmative actions in selection problems (e.g., college admission or hiring), a recent line of research proposed a model based on differential variance. This model assumes that the decision-maker has a noisy estimate of each candidate’s quality and puts forward the difference in the noise variances between different demographic groups as a key factor to explain discrimination. The literature on differential variance, however, does not consider the strategic behavior of candidates who can react to the selection procedure to improve their outcome, which is well-known to happen in many domains. In 22, we study how the strategic aspect affects fairness in selection problems. We propose to model selection problems with strategic candidates as a contest game: A population of rational candidates compete by choosing an effort level to increase their quality. They incur a cost-of-effort but get a (random) quality whose expectation equals the chosen effort. A Bayesian decision-maker observes a noisy estimate of the quality of each candidate (with differential variance) and selects the fraction α of best candidates based on their posterior expected quality; each selected candidate receives a reward S. We characterize the (unique) equilibrium of this game in the different parameters’ regimes, both when the decision-maker is unconstrained and when they are constrained to respect the fairness notion of demographic parity. Our results reveal important impacts of the strategic behavior on the discrimination observed at equilibrium and allow us to understand the effect of imposing demographic parity in this context. In particular, we find that, in many cases, the results contrast with the non-strategic setting. We also find that, when the cost-of-effort depends on the demographic group (which is reasonable in many cases), then it entirely governs the observed discrimination (i.e., the noise becomes a second-order effect that does not have any impact on discrimination). Finally we find that imposing demographic parity can sometimes increase the quality of the selection at equilibrium; which surprisingly contrasts with the optimality of the Bayesian decision-maker in the non-strategic case. Our results give a new perspective on fairness in selection problems, relevant in many domains where strategic behavior is a reality.

In 34, we consider the problem of linear regression from strategic data sources with a public good component, i.e., when data is provided by strategic agents who seek to minimize an individual provision cost for increasing their data's precision while benefiting from the model's overall precision. In contrast to previous works, our model tackles the case where there is uncertainty on the attributes characterizing the agents' data – a critical aspect of the problem when the number of agents is large. We provide a characterization of the game's equilibrium, which reveals an interesting connection with optimal design. Subsequently, we focus on the asymptotic behavior of the covariance of the linear regression parameters estimated via generalized least squares as the number of data sources becomes large. We provide upper and lower bounds for this covariance matrix and we show that, when the agents' provision costs are super-linear, the model's covariance converges to zero but at a slower rate relative to virtually all learning problems with exogenous data. On the other hand, if the agents' provision costs are linear, this covariance fails to converge. This shows that even the basic property of consistency of generalized least squares estimators is compromised when the data sources are strategic.

In 26, we consider the problem of computing a sequence of rankings that maximizes consumer-side utility while minimizing producer-side individual unfairness of exposure. While prior work has addressed this problem using linear or quadratic programs on bistochastic matrices, such approaches, relying on Birkhoff-von Neumann (BvN) decompositions, are too slow to be implemented at large scale. In this paper we introduce a geometrical object, a polytope that we call expohedron, whose points represent all achievable exposures of items for a Position Based Model (PBM). We exhibit some of its properties and lay out a Carathéodory decomposition algorithm with complexity $O(n^{2}log\left(n\right))$ able to express any point inside the expohedron as a convex sum of at most $n$ vertices, where $n$ is the number of items to rank. Such a decomposition makes it possible to express any feasible target exposure as a distribution over at most n rankings. Furthermore we show that we can use this polytope to recover the whole Pareto frontier of the multi-objective fairness-utility optimization problem, using a simple geometrical procedure with complexity $O(n^{2}log\left(n\right))$. Our approach compares favorably to linear or quadratic programming baselines in terms of algorithmic complexity and empirical runtime and is applicable to any merit that is a non-decreasing function of item relevance. Furthermore our solution can be expressed as a distribution over only $n$ permutations, instead of the ${(n-1)}^2+1$ achieved with BvN decompositions. We perform experiments on synthetic and real-world datasets, confirming our theoretical results.

In recent years, it has become clear that rankings delivered in many areas need not only be useful to the users but also respect fairness of exposure for the item producers. We consider the problem of finding ranking policies that achieve a Pareto-optimal tradeoff between these two aspects. Several methods were proposed to solve it; for instance a popular one is to use linear programming with a Birkhoffvon Neumann decomposition. These methods, however, are based on a classical Position Based exposure Model (PBM), which assumes independence between the items (hence the exposure only depends on the rank). In many applications, this assumption is unrealistic and the community increasingly moves towards considering other models that include dependencies, such as the Dynamic Bayesian Network (DBN) exposure model. For such models, computing (exact) optimal fair ranking policies remains an open question. In 27, we answer this question by leveraging a new geometrical method based on the so-called expohedron proposed recently for the PBM. We lay out the structure of a new geometrical object (the DBN-expohedron), and propose for it a Carathéodory decomposition algorithm of complexity $O\left(n^3\right)$, where $n$ is the number of documents to rank. Such an algorithm enables expressing any feasible expected exposure vector as a distribution over at most n rankings; furthermore we show that we can compute the whole set of Pareto-optimal expected exposure vectors with the same complexity $O\left(n^3\right)$. Our work constitutes the first exact algorithm able to efficiently find a Pareto-optimal distribution of rankings. It is applicable to a broad range of fairness notions, including classical notions of meritocratic and demographic fairness. We empirically evaluate our method on the TREC2020 and MSLR datasets and compare it to several baselines in terms of Pareto-optimality and speed.

10.1 International initiatives

10.2 International research visitors

10.3 European initiatives

10.4 National initiatives

Projects indicated with a $☆$ are projects coordinated by members of the POLARIS team.

11.1 Promoting scientific activities

11.2 Teaching - Supervision - Juries

11.3 Popularization

12.1 Publications of the year

12.2 Other

12.3 Cited publications

• 48 inproceedingsA.Athanasios Andreou, M.Marcio Silva, F.Fabrício Benevenuto, O.Oana Goga, P.Patrick Loiseau and A.Alan Mislove. Measuring the Facebook Advertising Ecosystem.NDSS 2019 - Proceedings of the Network and Distributed System Security SymposiumSan Diego, United StatesFebruary 2019, 1-15
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• 49 inproceedingsA.Athanasios Andreou, G.Giridhari Venkatadri, O.Oana Goga, K. P.Krishna P Gummadi, P.Patrick Loiseau and A.Alan Mislove. Investigating 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, 1-15
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• 50 articleJ.Jonatha Anselmi. Combining Size-Based Load Balancing with Round-Robin for Scalable Low Latency.IEEE Transactions on Parallel and Distributed Systems2019, 1-3
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• 51 articleJ.Jonatha Anselmi and J.Josu Doncel. Asymptotically Optimal Size-Interval Task Assignments.IEEE Transactions on Parallel and Distributed Systems30112019, 2422-2433
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• 52 articleJ.Jonatha Anselmi and F.François Dufour. Power-of-d-Choices with Memory: Fluid Limit and Optimality.Mathematics of Operations Research4532020, 862-888
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• 53 inproceedingsR. M.Rosa M. Badia, J.Jesús Labarta, J.Judit Giménez and F.Francesc Escalé. Dimemas: Predicting MPI Applications Behaviour in Grid Environments.Proc. of the Workshop on Grid Applications and Programming Tools2003
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• 54 conferenceS.Swen Böhm and C.Christian Engelmann. xSim: The Extreme-Scale Simulator.HPCSIstanbul, Turkey2011
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• 55 inproceedingsP.Pedro Bruel, S.Steven Quinito Masnada, B.Brice Videau, A.Arnaud Legrand, J.-M.Jean-Marc Vincent and A.Alfredo Goldman. Autotuning under Tight Budget Constraints: A Transparent Design of Experiments Approach.CCGrid 2019 - International Symposium in Cluster, Cloud, and Grid ComputingLarcana, CyprusIEEEMay 2019, 1-10
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• 56 incollectionH.Holger Brunst, D.Daniel Hackenberg, G.Guido Juckeland and H.Heide Rohling. Comprehensive Performance Tracking with VAMPIR 7.Tools for High Performance Computing 2009The paper details the latest improvements in the Vampir visualization tool.Springer Berlin Heidelberg2010
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• 57 articleP.Pierre COUCHENEY, B.Bruno Gaujal and P.Panayotis Mertikopoulos. Penalty-Regulated Dynamics and Robust Learning Procedures in Games.Mathematics of Operations Research4032015, 611-633
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• 58 articleG.Giuliano Casale and N.Nicolas Gast. Performance analysis methods for list-based caches with non-uniform access.IEEE/ACM Transactions on NetworkingDecember 2020, 1-18
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• 59 inproceedingsA.Abhijnan Chakraborty, G. K.Gourab K Patro, N.Niloy Ganguly, K. P.Krishna P Gummadi and P.Patrick Loiseau. Equality of Voice: Towards Fair Representation in Crowdsourced Top-K Recommendations.FAT* 2019 - ACM Conference on Fairness, Accountability, and TransparencyProceedings of the ACM Conference on Fairness, Accountability, and Transparency (FAT*)Atlanta, United StatesACMJanuary 2019, 129-138
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• 60 inproceedingsT.Tom Cornebize, A.Arnaud Legrand and F. C.Franz C Heinrich. Fast and Faithful Performance Prediction of MPI Applications: the HPL Case Study.2019 IEEE International Conference on Cluster Computing (CLUSTER)Albuquerque, United StatesSeptember 2019
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• 61 articleA.Augustin Degomme, A.Arnaud Legrand, G.Georges Markomanolis, M.Martin Quinson, M. L.Mark Lee Stillwell and F.Frédéric Suter. Simulating MPI applications: the SMPI approach.IEEE Transactions on Parallel and Distributed Systems288August 2017, 14
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• 62 inproceedingsB.Bruno Donassolo, I.Ilhem Fajjari, A.Arnaud Legrand and P.Panayotis Mertikopoulos. Load Aware Provisioning of IoT Services on Fog Computing Platform.IEEE International Conference on Communications (ICC)Shanghai, ChinaIEEEMay 2019
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• 63 inproceedings J.Josu Doncel, N.Nicolas Gast and B.Bruno Gaujal. Are mean-field games the limits of finite stochastic games? The 18th Workshop on MAthematical performance Modeling and Analysis Nice, France June 2016
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• 64 articleJ.Josu Doncel, N.Nicolas Gast and B.Bruno Gaujal. Discrete Mean Field Games: Existence of Equilibria and Convergence.Journal of Dynamics and Games632019, 1-19
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• 65 inproceedingsV.Vitalii Emelianov, G.George Arvanitakis, N.Nicolas Gast, K. P.Krishna P Gummadi and P.Patrick Loiseau. The Price of Local Fairness in Multistage Selection.IJCAI-2019 - Twenty-Eighth International Joint Conference on Artificial IntelligenceMacao, FranceInternational Joint Conferences on Artificial Intelligence OrganizationAugust 2019, 5836-5842
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• 66 inproceedingsV.Vitalii Emelianov, N.Nicolas Gast, K. P.Krishna P. Gummadi and P.Patrick Loiseau. On Fair Selection in the Presence of Implicit Variance.EC 2020 - Twenty-First ACM Conference on Economics and ComputationBudapest, HungaryACMJuly 2020, 649–675
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• 67 inproceedingsL.Lampros Flokas, E. V.Emmanouil V Vlatakis-Gkaragkounis, T.Thanasis Lianeas, P.Panayotis Mertikopoulos and G.Georgios Piliouras. No-regret learning and mixed Nash equilibria: They do not mix.NeurIPS 2020 - 34th International Conference on Neural Information Processing SystemsVancouver, CanadaDecember 2020, 1-24
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• 68 articleV.Vinicius Garcia Pinto, L. M.Lucas Mello Schnorr, L.Luka Stanisic, A.Arnaud Legrand, S.Samuel Thibault and V.Vincent Danjean. A Visual Performance Analysis Framework for Task-based Parallel Applications running on Hybrid Clusters.Concurrency and Computation: Practice and Experience3018April 2018, 1-31
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• 69 articleN.Nicolas Gast, L.Luca Bortolussi and M.Mirco Tribastone. Size Expansions of Mean Field Approximation: Transient and Steady-State Analysis.Performance Evaluation2018, 1-15
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• 70 inproceedingsN.Nicolas Gast. Expected Values Estimated via Mean-Field 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 '17Urbana-Champaign, United StatesJune 2017, 26
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• 71 unpublishedN.Nicolas Gast, B.Bruno Gaujal and C.Chen Yan. Exponential Convergence Rate for the Asymptotic Optimality of Whittle Index Policy.December 2020,
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• 72 inproceedingsN.Nicolas Gast and B. V.Benny Van Houdt. A Refined Mean Field Approximation.ACM SIGMETRICS 2018Irvine, United StatesJune 2018, 1
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• 73 articleN.Nicolas Gast, S.Stratis Ioannidis, P.Patrick Loiseau and B.Benjamin Roussillon. Linear Regression from Strategic Data Sources.ACM Transactions on Economics and Computation82May 2020, 1-24
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• 74 inproceedingsN.Nicolas Gast, D.Diego Latella and M.Mieke Massink. A Refined Mean Field Approximation for Synchronous Population Processes.MAMA 2018Workshop on MAthematical performance Modeling and AnalysisIrvine, United StatesJune 2018, 1-3
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• 75 inproceedingsN.Nicolas Gast and B.Benny Van Houdt. Asymptotically Exact TTL-Approximations of the Cache Replacement Algorithms LRU(m) and h-LRU.28th International Teletraffic Congress (ITC 28)Würzburg, GermanySeptember 2016
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• 76 articleN.Nicolas Gast and B.Benny Van Houdt. TTL Approximations of the Cache Replacement Algorithms LRU(m) and h-LRU.Performance EvaluationSeptember 2017
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• 77 inproceedingsB.Bruno Gaujal, J.Josu Doncel and N.Nicolas Gast. Vaccination in a Large Population: Mean Field Equilibrium versus Social Optimum.NETGCOOP 2020 - 10th International Conference on NETwork Games, COntrol and OPtimizationCargèse, FranceSeptember 2021, 1-9
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• 78 inproceedingsB.Bruno Gaujal, A.Alain Girault and S.Stéphan Plassart. A Linear Time Algorithm for Computing Off-line Speed Schedules Minimizing Energy Consumption.MSR 2019 - 12ème Colloque sur la Modélisation des Systèmes RéactifsAngers, FranceNovember 2019, 1-14
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• 79 inproceedingsB.Bruno Gaujal, A.Alain Girault and S.Stéphan Plassart. Discrete and Continuous Optimal Control for Energy Minimization in Real-Time Systems.EBCCSP 2020 - 6th International Conference on Event-Based Control, Communication, and Signal ProcessingKrakow, PolandIEEESeptember 2020, 1-8
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• 80 articleB.Bruno Gaujal, A.Alain Girault and S.Stéphan Plassart. Dynamic Speed Scaling Minimizing Expected Energy Consumption for Real-Time Tasks.Journal of SchedulingJuly 2020, 1-25
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• 81 techreportB.Bruno Gaujal, A.Alain Girault and S.Stéphan Plassart. Exploiting Job Variability to Minimize Energy Consumption under Real-Time Constraints.RR-9300Inria Grenoble Rhône-Alpes, Université de Grenoble ; Université Grenoble - AlpesNovember 2019, 23
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• 82 inproceedingsA.Angeliki Giannou, E. V.Emmanouil Vasileios Vlatakis-Gkaragkounis and P.Panayotis Mertikopoulos. Survival of the strictest: Stable and unstable equilibria under regularized learning with partial information.COLT 2021 - 34th Annual Conference on Learning TheoryBoulder, United StatesAugust 2021, 1-30
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• 83 articleM.MT Heath and J.JA Etheridge. Visualizing the performance of parallel programs.IEEE software85The paper presents Paragraph.1991
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• 84 inproceedingsF. C.Franz C. Heinrich, T.Tom Cornebize, A.Augustin Degomme, A.Arnaud Legrand, A.Alexandra Carpen-Amarie, S.Sascha Hunold, A.-C.Anne-Cécile Orgerie and M.Martin Quinson. Predicting the Energy Consumption of MPI Applications at Scale Using a Single Node.Cluster 2017IEEEHawaii, United StatesSeptember 2017
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• 85 inproceedingsT.Torsten Hoefler, T.Timo Schneider and A.Andrew Lumsdaine. LogGOPSim - Simulating Large-Scale Applications in the LogGOPS Model.ACM Workshop on Large-Scale System and Application Performance2010
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• 86 inproceedingsY.-P.Ya-Ping Hsieh, P.Panayotis Mertikopoulos and V.Volkan Cevher. The limits of min-max optimization algorithms: Convergence to spurious non-critical sets.ICML 2021 - 38th International Conference on Machine LearningVienna, AustriaJuly 2021
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• 87 articleL. V.Laxmikant V. Kalé, G.Gengbin Zheng, C. W.Chee Wai Lee and S.Sameer Kumar. Scaling applications to massively parallel machines using Projections performance analysis tool.Future Generation Comp. Syst.2232006
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