Representation Learning for General-sum Low-rank Markov Games

TL;DR

This paper introduces the first sample-efficient algorithms for multi-agent general-sum Markov games with nonlinear function approximation, leveraging representation learning to achieve near-optimal policies with deep learning-friendly methods.

Contribution

It presents novel model-based and model-free algorithms that efficiently learn representations and policies in complex multi-agent environments with theoretical guarantees.

Findings

Achieves poly$(H,d,A,1/\varepsilon)$ sample complexity for general-sum Markov games.

Develops an algorithm that handles large numbers of players by exploiting factorized transition structures.

Demonstrates neural network implementation and outperforms DQN with fictitious play in experiments.

Abstract

We study multi-agent general-sum Markov games with nonlinear function approximation. We focus on low-rank Markov games whose transition matrix admits a hidden low-rank structure on top of an unknown non-linear representation. The goal is to design an algorithm that (1) finds an $\varepsilon$-equilibrium policy sample efficiently without prior knowledge of the environment or the representation, and (2) permits a deep-learning friendly implementation. We leverage representation learning and present a model-based and a model-free approach to construct an effective representation from the collected data. For both approaches, the algorithm achieves a sample complexity of poly$(H,d,A,1/\varepsilon)$, where $H$ is the game horizon, $d$ is the dimension of the feature vector, $A$ is the size of the joint action space and $\varepsilon$ is the optimality gap. When the number of players is large, the above sample complexity can scale exponentially with the number of players in the worst case. To address this challenge, we consider Markov games with a factorized transition structure and present an algorithm that escapes such exponential scaling. To our best knowledge, this is the first sample-efficient algorithm for multi-agent general-sum Markov games that incorporates (non-linear) function approximation. We accompany our theoretical result with a neural network-based implementation of our algorithm and evaluate it against the widely used deep RL baseline, DQN with fictitious play.