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As a primary contribution, we present a convergence theorem for stochastic iterations, and in particular, Q-learning iterates, under a general, possibly non-Markovian, stochastic environment. Our conditions for convergence involve an…

Optimization and Control · Mathematics 2024-03-05 Ali Devran Kara , Serdar Yuksel

We use ideas from distributed computing and game theory to study dynamic and decentralized environments in which computational nodes, or decision makers, interact strategically and with limited information. In such environments, which arise…

Computer Science and Game Theory · Computer Science 2017-04-06 Aaron D. Jaggard , Neil Lutz , Michael Schapira , Rebecca N. Wright

Reinforcement learning (RL) algorithms can find an optimal policy for a single agent to accomplish a particular task. However, many real-world problems require multiple agents to collaborate in order to achieve a common goal. For example, a…

Machine Learning · Computer Science 2025-10-20 Jan Corazza , Hadi Partovi Aria , Hyohun Kim , Daniel Neider , Zhe Xu

The goal of this paper is to analyze distributional Markov Decision Processes as a class of control problems in which the objective is to learn policies that steer the distribution of a cumulative reward toward a prescribed target law,…

Optimization and Control · Mathematics 2026-02-09 Nicole Bäuerle , Athanasios Vasileiadis

As quantum processors advance, the emergence of large-scale decentralized systems involving interacting quantum-enabled agents is on the horizon. Recent research efforts have explored quantum versions of Nash and correlated equilibria as…

Computer Science and Game Theory · Computer Science 2024-12-18 Wayne Lin , Georgios Piliouras , Ryann Sim , Antonios Varvitsiotis

In Markov decision processes (MDPs), quantile risk measures such as Value-at-Risk are a standard metric for modeling RL agents' preferences for certain outcomes. This paper proposes a new Q-learning algorithm for quantile optimization in…

Machine Learning · Computer Science 2024-11-01 Jia Lin Hau , Erick Delage , Esther Derman , Mohammad Ghavamzadeh , Marek Petrik

We consider two-player zero-sum stochastic games and propose a two-timescale $Q$-learning algorithm with function approximation that is payoff-based, convergent, rational, and symmetric between the two players. In two-timescale…

Machine Learning · Computer Science 2023-12-11 Zaiwei Chen , Kaiqing Zhang , Eric Mazumdar , Asuman Ozdaglar , Adam Wierman

This paper is concerned with the linear quadratic optimal control of discrete-time time-varying system with terminal state constraint. The main contribution is to propose a Q-learning algorithm for the optimal controller when the…

Optimization and Control · Mathematics 2023-07-20 Juanjuan Xu , Jingmei Liu , Zhaorong Zhang , Wei Wang

This paper considers the discounted criterion of nonzero-sum decentralized stochastic games with prospect players. The state and action spaces are finite. The state transition probability is nonstationary. Each player independently controls…

Optimization and Control · Mathematics 2024-05-16 Yiting Wu , Junyu Zhang

A key task in Artificial Intelligence is learning effective policies for controlling agents in unknown environments to optimize performance measures. Off-policy learning methods, like Q-learning, allow learners to make optimal decisions…

Artificial Intelligence · Computer Science 2025-10-27 Mingxuan Li , Junzhe Zhang , Elias Bareinboim

Multi-player multi-armed bandit is an increasingly relevant decision-making problem, motivated by applications to cognitive radio systems. Most research for this problem focuses exclusively on the settings that players have \textit{full…

Machine Learning · Computer Science 2022-12-14 Guojun Xiong , Jian Li

Advances in low-communication training algorithms are enabling a shift from centralised model training to compute setups that are either distributed across multiple clusters or decentralised via community-driven contributions. This paper…

Computers and Society · Computer Science 2025-07-11 Jakub Kryś , Yashvardhan Sharma , Janet Egan

The $Q$-learning algorithm is a simple and widely-used stochastic approximation scheme for reinforcement learning, but the basic protocol can exhibit instability in conjunction with function approximation. Such instability can be observed…

Machine Learning · Computer Science 2022-06-03 Andrea Zanette , Martin J. Wainwright

This paper studies a linear-quadratic mean-field game of stochastic large-population system, where the large-population system satisfies a class of $N$ weakly coupled linear backward stochastic differential equation. Different from the…

Optimization and Control · Mathematics 2024-12-02 Yu Si , Jingtao Shi

Engineering system design, viewed as a decision-making process, faces challenges due to complexity and uncertainty. In this paper, we present a framework proposing the use of the Deep Q-learning algorithm to optimize the design of…

Machine Learning · Computer Science 2024-01-01 Ramin Giahi , Cameron A. MacKenzie , Reyhaneh Bijari

In this paper, we consider a large class of constrained non-cooperative stochastic Markov games with countable state spaces and discounted cost criteria. In one-player case, i.e., constrained discounted Markov decision models, it is…

Optimization and Control · Mathematics 2021-12-16 Anna Jaśkiewicz , Andrzej S. Nowak

A major challenge of multiagent reinforcement learning (MARL) is the curse of multiagents, where the size of the joint action space scales exponentially with the number of agents. This remains to be a bottleneck for designing efficient MARL…

Machine Learning · Computer Science 2021-10-28 Chi Jin , Qinghua Liu , Yuanhao Wang , Tiancheng Yu

The behaviour of multi-agent learning in many player games has been shown to display complex dynamics outside of restrictive examples such as network zero-sum games. In addition, it has been shown that convergent behaviour is less likely to…

Computer Science and Game Theory · Computer Science 2023-07-27 Aamal Hussain , Dan Leonte , Francesco Belardinelli , Georgios Piliouras

Achieving convergence of multiple learning agents in general $N$-player games is imperative for the development of safe and reliable machine learning (ML) algorithms and their application to autonomous systems. Yet it is known that, outside…

Computer Science and Game Theory · Computer Science 2023-01-24 Aamal Abbas Hussain , Francesco Belardinelli , Georgios Piliouras

Decentralized machine learning often relies on outsourcing computations, such as gradient evaluations, to untrusted worker nodes. Existing robust aggregation methods can mitigate malicious behavior under honest-majority assumptions, but may…

Machine Learning · Computer Science 2026-05-11 Hanzaleh Akbari Nodehi , Parsa Moradi , Soheil Mohajer , Mohammad Ali Maddah-Ali