Multi-Agent Reinforcement Learning with Reward Delays

TL;DR

This paper introduces MARL algorithms capable of efficiently handling reward delays, both finite and infinite, with proven convergence rates and equilibrium guarantees, advancing the robustness of multi-agent learning in delayed reward settings.

Contribution

The paper develops novel MARL algorithms based on V-learning that effectively manage reward delays, providing theoretical convergence rates and extending to infinite delays with a reward skipping scheme.

Findings

Achieves convergence to coarse correlated equilibrium with explicit rate.

Extends to infinite delays with a reward skipping scheme.

Provides theoretical analysis of delay impact on learning performance.

Abstract

This paper considers multi-agent reinforcement learning (MARL) where the rewards are received after delays and the delay time varies across agents and across time steps. Based on the V-learning framework, this paper proposes MARL algorithms that efficiently deal with reward delays. When the delays are finite, our algorithm reaches a coarse correlated equilibrium (CCE) with rate $\tilde{\mathcal{O}}(\frac{H^3\sqrt{S\mathcal{T}_K}}{K}+\frac{H^3\sqrt{SA}}{\sqrt{K}})$ where $K$ is the number of episodes, $H$ is the planning horizon, $S$ is the size of the state space, $A$ is the size of the largest action space, and $\mathcal{T}_K$ is the measure of total delay formally defined in the paper. Moreover, our algorithm is extended to cases with infinite delays through a reward skipping scheme. It achieves convergence rate similar to the finite delay case.