A Generalized Training Approach for Multiagent Learning

TL;DR

This paper extends the PSRO multiagent training framework to general-sum, many-player games using $ ext{α}$-Rank, providing convergence guarantees and demonstrating superior performance in complex poker and MuJoCo soccer environments.

Contribution

It introduces $ ext{α}$-Rank into PSRO for general-sum, many-player games, offering convergence guarantees and improved scalability over Nash-based methods.

Findings

$ ext{α}$-Rank-based PSRO converges faster than Nash-based PSRO in multi-player poker.

The approach is effective in complex domains like MuJoCo soccer.

Theoretical guarantees are established for several game classes.

Abstract

This paper investigates a population-based training regime based on game-theoretic principles called Policy-Spaced Response Oracles (PSRO). PSRO is general in the sense that it (1) encompasses well-known algorithms such as fictitious play and double oracle as special cases, and (2) in principle applies to general-sum, many-player games. Despite this, prior studies of PSRO have been focused on two-player zero-sum games, a regime wherein Nash equilibria are tractably computable. In moving from two-player zero-sum games to more general settings, computation of Nash equilibria quickly becomes infeasible. Here, we extend the theoretical underpinnings of PSRO by considering an alternative solution concept, $\alpha$-Rank, which is unique (thus faces no equilibrium selection issues, unlike Nash) and applies readily to general-sum, many-player settings. We establish convergence guarantees in several games classes, and identify links between Nash equilibria and $\alpha$-Rank. We demonstrate the competitive performance of $\alpha$-Rank-based PSRO against an exact Nash solver-based PSRO in 2-player Kuhn and Leduc Poker. We then go beyond the reach of prior PSRO applications by considering 3- to 5-player poker games, yielding instances where $\alpha$-Rank achieves faster convergence than approximate Nash solvers, thus establishing it as a favorable general games solver. We also carry out an initial empirical validation in MuJoCo soccer, illustrating the feasibility of the proposed approach in another complex domain.