AWESOME: A General Multiagent Learning Algorithm that Converges in Self-Play and Learns a Best Response Against Stationary Opponents

TL;DR

AWESOME is a novel multiagent learning algorithm that guarantees convergence to Nash equilibrium in all finite repeated games and adapts to stationary opponents, requiring only action observation.

Contribution

It introduces the first algorithm with proven convergence and optimal play in all repeated finite games, even against opponents who become stationary.

Findings

Guarantees convergence to Nash equilibrium in all finite repeated games.

Learns to play optimally against stationary opponents.

Requires only observation of opponents' actions, not strategies.

Abstract

A satisfactory multiagent learning algorithm should, {\em at a minimum}, learn to play optimally against stationary opponents and converge to a Nash equilibrium in self-play. The algorithm that has come closest, WoLF-IGA, has been proven to have these two properties in 2-player 2-action repeated games--assuming that the opponent's (mixed) strategy is observable. In this paper we present AWESOME, the first algorithm that is guaranteed to have these two properties in {\em all} repeated (finite) games. It requires only that the other players' actual actions (not their strategies) can be observed at each step. It also learns to play optimally against opponents that {\em eventually become} stationary. The basic idea behind AWESOME ({\em Adapt When Everybody is Stationary, Otherwise Move to Equilibrium}) is to try to adapt to the others' strategies when they appear stationary, but otherwise to retreat to a precomputed equilibrium strategy. The techniques used to prove the properties of AWESOME are fundamentally different from those used for previous algorithms, and may help in analyzing other multiagent learning algorithms also.