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Reciprocity is an important feature of human social interaction and underpins our cooperative nature. What is more, simple forms of reciprocity have proved remarkably resilient in matrix game social dilemmas. Most famously, the tit-for-tat…
Adversarial self-play in two-player games has delivered impressive results when used with reinforcement learning algorithms that combine deep neural networks and tree search. Algorithms like AlphaZero and Expert Iteration learn tabula-rasa,…
This paper investigates a class of multi-player discrete games where each player aims to maximize its own utility function. Each player does not know the other players' action sets, their deployed actions or the structures of its own or the…
Learning in games considers how multiple agents maximize their own rewards through repeated games. Memory, an ability that an agent changes his/her action depending on the history of actions in previous games, is often introduced into…
Growing advancements in reinforcement learning has led to advancements in control theory. Reinforcement learning has effectively solved the inverted pendulum problem and more recently the double inverted pendulum problem. In reinforcement…
We consider centralized and distributed mirror descent algorithms over a finite-dimensional Hilbert space, and prove that the problem variables converge to an optimizer of a possibly nonsmooth function when the step sizes are square…
First-order optimization methods tend to inherently favor certain solutions over others when minimizing an underdetermined training objective that has multiple global optima. This phenomenon, known as implicit bias, plays a critical role in…
We study online learning and equilibrium computation in games with polyhedral decision sets, a property shared by both normal-form games and extensive-form games (EFGs), when the learning agent is restricted to using a best-response oracle.…
Bayesian regression games are a special class of two-player general-sum Bayesian games in which the learner is partially informed about the adversary's objective through a Bayesian prior. This formulation captures the uncertainty in regard…
Mean Field Games (MFGs) have been introduced to efficiently approximate games with very large populations of strategic agents. Recently, the question of learning equilibria in MFGs has gained momentum, particularly using model-free…
Self-play, where the algorithm learns by playing against itself without requiring any direct supervision, has become the new weapon in modern Reinforcement Learning (RL) for achieving superhuman performance in practice. However, the…
This paper proposes new, end-to-end deep reinforcement learning algorithms for learning two-player zero-sum Markov games. Different from prior efforts on training agents to beat a fixed set of opponents, our objective is to find the Nash…
Many tasks in modern machine learning can be formulated as finding equilibria in \emph{sequential} games. In particular, two-player zero-sum sequential games, also known as minimax optimization, have received growing interest. It is…
Many real-world applications involve some agents that fall into two teams, with payoffs that are equal within the same team but of opposite sign across the opponent team. The so-called two-team zero-sum Markov games (2t0sMGs) can be…
Many recent AI architectures are inspired by zero-sum games, however, the behavior of their dynamics is still not well understood. Inspired by this, we study standard gradient descent ascent (GDA) dynamics in a specific class of non-convex…
This paper investigates posterior sampling algorithms for competitive reinforcement learning (RL) in the context of general function approximations. Focusing on zero-sum Markov games (MGs) under two critical settings, namely self-play and…
We study the problem of learning Nash equilibria in offline two-player zero-sum Markov games. While existing approaches often rely on explicit pessimism to address distribution shift, we show that KL regularization alone suffices to…
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…
We introduce a simple extensive-form algorithm for finding equilibria of two-player, zero-sum games. The algorithm is realization equivalent to a generalized form of Fictitious Play. We compare its performance to that of a similar…
Mirror descent is a well established tool for solving convex optimization problems with convex constraints. This article introduces continuous-time mirror descent dynamics for approximating optimal Markov controls for stochastic control…