Leveraging repeated games for solving complex multiagent decision problems

Prendre de bonnes décisions dans des environnements multiagents est une tâche difficile dans la mesure où la présence de plusieurs décideurs implique des conflits d'intérêts, un manque de coordination, et une multiplicité de décisions possibles. Si de plus, les décideurs interagissent successivement à travers le temps, ils doivent non seulement décider ce qu'il faut faire actuellement, mais aussi comment leurs décisions actuelles peuvent affecter le comportement des autres dans le futur. La théorie des jeux est un outil mathématique qui vise à modéliser ce type d'interactions via des jeux stratégiques à plusieurs joueurs. Des lors, les problèmes de décision multiagent sont souvent étudiés en utilisant la théorie des jeux. Dans ce contexte, et si on se restreint aux jeux dynamiques, les problèmes de décision multiagent complexes peuvent être approchés de façon algorithmique. La contribution de cette thèse est triple. Premièrement, elle contribue à un cadre algorithmique pour la planification distribuée dans les jeux dynamiques non-coopératifs. La multiplicité des plans possibles est à l'origine de graves complications pour toute approche de planification. Nous proposons une nouvelle approche basée sur la notion d'apprentissage dans les jeux répétés. Une telle approche permet de surmonter lesdites complications par le biais de la communication entre les joueurs. Nous proposons ensuite un algorithme d'apprentissage pour les jeux répétés en ``self-play''. Notre algorithme permet aux joueurs de converger, dans les jeux répétés initialement inconnus, vers un comportement conjoint optimal dans un certain sens bien défini, et ce, sans aucune communication entre les joueurs. Finalement, nous proposons une famille d'algorithmes de résolution approximative des jeux dynamiques et d'extraction des stratégies des joueurs. Dans ce contexte, nous proposons tout d'abord une méthode pour calculer un sous-ensemble non vide des équilibres approximatifs parfaits en sous-jeu dans les jeux répétés. Nous montrons ensuite comment nous pouvons étendre cette méthode pour approximer tous les équilibres parfaits en sous-jeu dans les jeux répétés, et aussi résoudre des jeux dynamiques plus complexes.Making good decisions in multiagent environments is a hard problem in the sense that the presence of several decision makers implies conflicts of interests, a lack of coordination, and a multiplicity of possible decisions. If, then, the same decision makers interact continuously through time, they have to decide not only what to do in the present, but also how their present decisions may affect the behavior of the others in the future. Game theory is a mathematical tool that aims to model such interactions as strategic games of multiple players. Therefore, multiagent decision problems are often studied using game theory. In this context, and being restricted to dynamic games, complex multiagent decision problems can be algorithmically approached. The contribution of this thesis is three-fold. First, this thesis contributes an algorithmic framework for distributed planning in non-cooperative dynamic games. The multiplicity of possible plans is a matter of serious complications for any planning approach. We propose a novel approach based on the concept of learning in repeated games. Our approach permits overcoming the aforementioned complications by means of communication between players. We then propose a learning algorithm for repeated game self-play. Our algorithm allows players to converge, in an initially unknown repeated game, to a joint behavior optimal in a certain, well-defined sense, without communication between players. Finally, we propose a family of algorithms for approximately solving dynamic games, and for extracting equilibrium strategy profiles. In this context, we first propose a method to compute a nonempty subset of approximate subgame-perfect equilibria in repeated games. We then demonstrate how to extend this method for approximating all subgame-perfect equilibria in repeated games, and also for solving more complex dynamic games

Adaptive Dynamics Learning and Q-initialization in the context of multiagent learning

L’apprentissage multiagent est une direction prometteuse de la recherche récente et à venir dans le contexte des systèmes intelligents. Si le cas mono-agent a été beaucoup étudié pendant les deux dernières décennies, le cas multiagent a été peu étudié vu sa complexité. Lorsque plusieurs agents autonomes apprennent et agissent simultanément, l’environnement devient strictement imprévisible et toutes les suppositions qui sont faites dans le cas mono-agent, telles que la stationnarité et la propriété markovienne, s’avèrent souvent inapplicables dans le contexte multiagent. Dans ce travail de maîtrise nous étudions ce qui a été fait dans ce domaine de recherches jusqu’ici, et proposons une approche originale à l’apprentissage multiagent en présence d’agents adaptatifs. Nous expliquons pourquoi une telle approche donne les résultats prometteurs lorsqu’on la compare aux différentes autres approches existantes. Il convient de noter que l’un des problèmes les plus ardus des algorithmes modernes d’apprentissage multiagent réside dans leur complexité computationnelle qui est fort élevée. Ceci est dû au fait que la taille de l’espace d’états du problème multiagent est exponentiel en le nombre d’agents qui agissent dans cet environnement. Dans ce travail, nous proposons une nouvelle approche de la réduction de la complexité de l’apprentissage par renforcement multiagent. Une telle approche permet de réduire de manière significative la partie de l’espace d’états visitée par les agents pour apprendre une solution efficace. Nous évaluons ensuite nos algorithmes sur un ensemble d’essais empiriques et présentons des résultats théoriques préliminaires qui ne sont qu’une première étape pour former une base de la validité de nos approches de l’apprentissage multiagent.Multiagent learning is a promising direction of the modern and future research in the context of intelligent systems. While the single-agent case has been well studied in the last two decades, the multiagent case has not been broadly studied due to its complex- ity. When several autonomous agents learn and act simultaneously, the environment becomes strictly unpredictable and all assumptions that are made in single-agent case, such as stationarity and the Markovian property, often do not hold in the multiagent context. In this Master’s work we study what has been done in this research field, and propose an original approach to multiagent learning in presence of adaptive agents. We explain why such an approach gives promising results by comparing it with other different existing approaches. It is important to note that one of the most challenging problems of all multiagent learning algorithms is their high computational complexity. This is due to the fact that the state space size of multiagent problem is exponential in the number of agents acting in the environment. In this work we propose a novel approach to the complexity reduction of the multiagent reinforcement learning. Such an approach permits to significantly reduce the part of the state space needed to be visited by the agents to learn an efficient solution. Then we evaluate our algorithms on a set of empirical tests and give a preliminary theoretical result, which is first step in forming the basis of validity of our approaches to multiagent learning

Many-agent Reinforcement Learning

Multi-agent reinforcement learning (RL) solves the problem of how each agent should behave optimally in a stochastic environment in which multiple agents are learning simultaneously. It is an interdisciplinary domain with a long history that lies in the joint area of psychology, control theory, game theory, reinforcement learning, and deep learning. Following the remarkable success of the AlphaGO series in single-agent RL, 2019 was a booming year that witnessed significant advances in multi-agent RL techniques; impressive breakthroughs have been made on developing AIs that outperform humans on many challenging tasks, especially multi-player video games. Nonetheless, one of the key challenges of multi-agent RL techniques is the scalability; it is still non-trivial to design efficient learning algorithms that can solve tasks including far more than two agents ($N \gg 2$), which I name by \emph{many-agent reinforcement learning} (MARL\footnote{I use the world of ``MARL" to denote multi-agent reinforcement learning with a particular focus on the cases of many agents; otherwise, it is denoted as ``Multi-Agent RL" by default.}) problems. In this thesis, I contribute to tackling MARL problems from four aspects. Firstly, I offer a self-contained overview of multi-agent RL techniques from a game-theoretical perspective. This overview fills the research gap that most of the existing work either fails to cover the recent advances since 2010 or does not pay adequate attention to game theory, which I believe is the cornerstone to solving many-agent learning problems. Secondly, I develop a tractable policy evaluation algorithm -- $\alpha^\alpha$-Rank -- in many-agent systems. The critical advantage of $\alpha^\alpha$-Rank is that it can compute the solution concept of $\alpha$-Rank tractably in multi-player general-sum games with no need to store the entire pay-off matrix. This is in contrast to classic solution concepts such as Nash equilibrium which is known to be $PPAD$-hard in even two-player cases. $\alpha^\alpha$-Rank allows us, for the first time, to practically conduct large-scale multi-agent evaluations. Thirdly, I introduce a scalable policy learning algorithm -- mean-field MARL -- in many-agent systems. The mean-field MARL method takes advantage of the mean-field approximation from physics, and it is the first provably convergent algorithm that tries to break the curse of dimensionality for MARL tasks. With the proposed algorithm, I report the first result of solving the Ising model and multi-agent battle games through a MARL approach. Fourthly, I investigate the many-agent learning problem in open-ended meta-games (i.e., the game of a game in the policy space). Specifically, I focus on modelling the behavioural diversity in meta-games, and developing algorithms that guarantee to enlarge diversity during training. The proposed metric based on determinantal point processes serves as the first mathematically rigorous definition for diversity. Importantly, the diversity-aware learning algorithms beat the existing state-of-the-art game solvers in terms of exploitability by a large margin. On top of the algorithmic developments, I also contribute two real-world applications of MARL techniques. Specifically, I demonstrate the great potential of applying MARL to study the emergent population dynamics in nature, and model diverse and realistic interactions in autonomous driving. Both applications embody the prospect that MARL techniques could achieve huge impacts in the real physical world, outside of purely video games