Modeling Mutual Influence in Multi-Agent Reinforcement Learning

In multi-agent systems (MAS), agents rarely act in isolation but tend to achieve their goals through interactions with other agents. To be able to achieve their ultimate goals, individual agents should actively evaluate the impacts on themselves of other agents' behaviors before they decide which actions to take. The impacts are reciprocal, and it is of great interest to model the mutual influence of agent's impacts with one another when they are observing the environment or taking actions in the environment. In this thesis, assuming that the agents are aware of each other's existence and their potential impact on themselves, I develop novel multi-agent reinforcement learning (MARL) methods that can measure the mutual influence between agents to shape learning. The first part of this thesis outlines the framework of recursive reasoning in deep multi-agent reinforcement learning. I hypothesize that it is beneficial for each agent to consider how other agents react to their behavior. I start from Probabilistic Recursive Reasoning (PR2) using level-1 reasoning and adopt variational Bayes methods to approximate the opponents' conditional policies. Each agent shapes the individual Q-value by marginalizing the conditional policies in the joint Q-value and finding the best response to improving their policies. I further extend PR2 to Generalized Recursive Reasoning (GR2) with different hierarchical levels of rationality. GR2 enables agents to possess various levels of thinking ability, thereby allowing higher-level agents to best respond to less sophisticated learners. The first part of the thesis shows that eliminating the joint Q-value to an individual Q-value via explicitly recursive reasoning would benefit the learning. In the second part of the thesis, in reverse, I measure the mutual influence by approximating the joint Q-value based on the individual Q-values. I establish Q-DPP, an extension of the Determinantal Point Process (DPP) with partition constraints, and apply it to multi-agent learning as a function approximator for the centralized value function. An attractive property of using Q-DPP is that when it reaches the optimum value, it can offer a natural factorization of the centralized value function, representing both quality (maximizing reward) and diversity (different behaviors). In the third part of the thesis, I depart from the action-level mutual influence and build a policy-space meta-game to analyze agents' relationship between adaptive policies. I present a Multi-Agent Trust Region Learning (MATRL) algorithm that augments single-agent trust region policy optimization with a weak stable fixed point approximated by the policy-space meta-game. The algorithm aims to find a game-theoretic mechanism to adjust the policy optimization steps that force the learning of all agents toward the stable point

von Neumann-Morgenstern and Savage Theorems for Causal Decision Making

Causal thinking and decision making under uncertainty are fundamental aspects of intelligent reasoning. Decision making under uncertainty has been well studied when information is considered at the associative (probabilistic) level. The classical Theorems of von Neumann-Morgenstern and Savage provide a formal criterion for rational choice using purely associative information. Causal inference often yields uncertainty about the exact causal structure, so we consider what kinds of decisions are possible in those conditions. In this work, we consider decision problems in which available actions and consequences are causally connected. After recalling a previous causal decision making result, which relies on a known causal model, we consider the case in which the causal mechanism that controls some environment is unknown to a rational decision maker. In this setting we state and prove a causal version of Savage's Theorem, which we then use to develop a notion of causal games with its respective causal Nash equilibrium. These results highlight the importance of causal models in decision making and the variety of potential applications.Comment: Submitted to Journal of Causal Inferenc

A Regularized Opponent Model with Maximum Entropy Objective

In a single-agent setting, reinforcement learning (RL) tasks can be cast into an inference problem by introducing a binary random variable o, which stands for the "optimality". In this paper, we redefine the binary random variable o in multi-agent setting and formalize multi-agent reinforcement learning (MARL) as probabilistic inference. We derive a variational lower bound of the likelihood of achieving the optimality and name it as Regularized Opponent Model with Maximum Entropy Objective (ROMMEO). From ROMMEO, we present a novel perspective on opponent modeling and show how it can improve the performance of training agents theoretically and empirically in cooperative games. To optimize ROMMEO, we first introduce a tabular Q-iteration method ROMMEO-Q with proof of convergence. We extend the exact algorithm to complex environments by proposing an approximate version, ROMMEO-AC. We evaluate these two algorithms on the challenging iterated matrix game and differential game respectively and show that they can outperform strong MARL baselines.Comment: Accepted to International Joint Conference on Artificial Intelligence (IJCA2019