Filtered Fictitious Play for Perturbed Observation Potential Games and Decentralised POMDPs

TL;DR

This paper introduces filtered fictitious play, an algorithm designed to handle noisy observations in potential games and Dec-POMDPs, demonstrating improved convergence and performance over existing methods in noisy environments.

Contribution

The paper develops filtered fictitious play to ensure convergence in noisy potential games and applies it to Dec-POMDPs, outperforming current solvers under observation noise.

Findings

Filtered fictitious play converges to Nash equilibrium despite observation noise.

The new method outperforms state-of-the-art Dec-POMDP solvers by 100% on average.

The approach is validated in a box pushing problem with noisy observations.

Abstract

Potential games and decentralised partially observable MDPs (Dec-POMDPs) are two commonly used models of multi-agent interaction, for static optimisation and sequential decisionmaking settings, respectively. In this paper we introduce filtered fictitious play for solving repeated potential games in which each player's observations of others' actions are perturbed by random noise, and use this algorithm to construct an online learning method for solving Dec-POMDPs. Specifically, we prove that noise in observations prevents standard fictitious play from converging to Nash equilibrium in potential games, which also makes fictitious play impractical for solving Dec-POMDPs. To combat this, we derive filtered fictitious play, and provide conditions under which it converges to a Nash equilibrium in potential games with noisy observations. We then use filtered fictitious play to construct a solver for Dec-POMDPs, and demonstrate our new algorithm's performance in a box pushing problem. Our results show that we consistently outperform the state-of-the-art Dec-POMDP solver by an average of 100% across the range of noise in the observation function.