Finite-Time Analysis of Asynchronous Multi-Agent TD Learning

TL;DR

This paper proves that asynchronous multi-agent TD learning algorithms can achieve linear convergence speedup similar to synchronous ones, even with delays, in a policy evaluation setting.

Contribution

First analysis of finite-time convergence for asynchronous multi-agent TD learning with delays, demonstrating linear speedup in convergence rate.

Findings

Asynchronous delays do not prevent linear convergence speedup.

Finite-time analysis accounts for time-varying delays.

AsyncMATD achieves similar convergence rates as synchronous algorithms.

Abstract

Recent research endeavours have theoretically shown the beneficial effect of cooperation in multi-agent reinforcement learning (MARL). In a setting involving $N$ agents, this beneficial effect usually comes in the form of an $N$-fold linear convergence speedup, i.e., a reduction - proportional to $N$ - in the number of iterations required to reach a certain convergence precision. In this paper, we show for the first time that this speedup property also holds for a MARL framework subject to asynchronous delays in the local agents' updates. In particular, we consider a policy evaluation problem in which multiple agents cooperate to evaluate a common policy by communicating with a central aggregator. In this setting, we study the finite-time convergence of \texttt{AsyncMATD}, an asynchronous multi-agent temporal difference (TD) learning algorithm in which agents' local TD update directions are subject to asynchronous bounded delays. Our main contribution is providing a finite-time analysis of \texttt{AsyncMATD}, for which we establish a linear convergence speedup while highlighting the effect of time-varying asynchronous delays on the resulting convergence rate.