Learning Rationalizable Equilibria in Multiplayer Games

TL;DR

This paper introduces efficient algorithms for learning rationalizable equilibria in multiplayer games with polynomial sample complexity, advancing multiagent learning by addressing previous exponential sample requirements.

Contribution

It presents the first polynomial-sample algorithms for rationalizable CCE and CE in multiplayer games, and introduces a new algorithm for finding rationalizable actions with improved sample complexity.

Findings

Algorithms achieve polynomial sample complexity for rationalizable CCE and CE.

Developed a new efficient algorithm for finding rationalizable actions.

Provided a lower bound confirming the optimality of their sample complexity.

Abstract

A natural goal in multiagent learning besides finding equilibria is to learn rationalizable behavior, where players learn to avoid iteratively dominated actions. However, even in the basic setting of multiplayer general-sum games, existing algorithms require a number of samples exponential in the number of players to learn rationalizable equilibria under bandit feedback. This paper develops the first line of efficient algorithms for learning rationalizable Coarse Correlated Equilibria (CCE) and Correlated Equilibria (CE) whose sample complexities are polynomial in all problem parameters including the number of players. To achieve this result, we also develop a new efficient algorithm for the simpler task of finding one rationalizable action profile (not necessarily an equilibrium), whose sample complexity substantially improves over the best existing results of Wu et al. (2021). Our algorithms incorporate several novel techniques to guarantee rationalizability and no (swap-)regret simultaneously, including a correlated exploration scheme and adaptive learning rates, which may be of independent interest. We complement our results with a sample complexity lower bound showing the sharpness of our guarantees.