Related papers: Almost Optimal Algorithms for Two-player Zero-Sum …
We study what dataset assumption permits solving offline two-player zero-sum Markov games. In stark contrast to the offline single-agent Markov decision process, we show that the single strategy concentration assumption is insufficient for…
We describe a new complete algorithm for computing Nash equilibrium in multiplayer general-sum games, based on a quadratically-constrained feasibility program formulation. We demonstrate that the algorithm runs significantly faster than the…
Continuous games are multiplayer games in which strategy sets are compact and utility functions are continuous. These games typically have a highly complicated structure of Nash equilibria, and numerical methods for the equilibrium…
Learning Markov decision processes (MDPs) in the presence of the adversary is a challenging problem in reinforcement learning (RL). In this paper, we study RL in episodic MDPs with adversarial reward and full information feedback, where the…
We give a simple proof of the well-known result that the marginal strategies of a coarse correlated equilibrium form a Nash equilibrium in two-player zero-sum games. A corollary of this fact is that no-external-regret learning algorithms…
In this paper, we investigate the seeking of Nash equilibrium (NE) in a non-cooperative quadratic game where all agents exchange their delayed strategy information with their neighbors. To extend best-response algorithms to the delayed…
Motivated by Generative Adversarial Networks, we study the computation of Nash equilibrium in concave network zero-sum games (NZSGs), a multiplayer generalization of two-player zero-sum games first proposed with linear payoffs. Extending…
This paper provides the first expert sample complexity characterization for learning a Nash equilibrium from expert data in Markov Games. We show that a new quantity named the single policy deviation concentrability coefficient is…
Nash Equilibrium (NE) is the canonical solution concept of game theory, which provides an elegant tool to understand the rationalities. Though mixed strategy NE exists in any game with finite players and actions, computing NE in two- or…
Consider a strongly monotone game where the players' utility functions include a reward function and a linear term for each dimension, with coefficients that are controlled by the manager. Gradient play converges to a unique Nash…
We propose a framework to compute approximate Nash equilibria in integer programming games with nonlinear payoffs, i.e., simultaneous and non-cooperative games where each player solves a parametrized mixed-integer nonlinear program. We…
Most existing results about \emph{last-iterate convergence} of learning dynamics are limited to two-player zero-sum games, and only apply under rigid assumptions about what dynamics the players follow. In this paper we provide new results…
This paper investigates the problem of computing the equilibrium of competitive games, which is often modeled as a constrained saddle-point optimization problem with probability simplex constraints. Despite recent efforts in understanding…
We show that, for any sufficiently small fixed $\epsilon > 0$, when both players in a general-sum two-player (bimatrix) game employ optimistic mirror descent (OMD) with smooth regularization, learning rate $\eta = O(\epsilon^2)$ and $T =…
Mean Field Games (MFGs) have the ability to handle large-scale multi-agent systems, but learning Nash equilibria in MFGs remains a challenging task. In this paper, we propose a deep reinforcement learning (DRL) algorithm that achieves…
Designing efficient algorithms to find Nash equilibrium (NE) refinements in sequential games is of paramount importance in practice. Indeed, it is well known that the NE has several weaknesses, since it may prescribe to play sub-optimal…
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…
We consider the problem of decentralized multi-agent reinforcement learning in Markov games. A fundamental question is whether there exist algorithms that, when adopted by all agents and run independently in a decentralized fashion, lead to…
In single-agent Markov decision processes, an agent can optimize its policy based on the interaction with environment. In multi-player Markov games (MGs), however, the interaction is non-stationary due to the behaviors of other players, so…
Provably efficient and robust equilibrium computation in general-sum Markov games remains a core challenge in multi-agent reinforcement learning. Nash equilibrium is computationally intractable in general and brittle due to equilibrium…