Finite- Time Analysis of Asynchronous Multi-Agent TD Learning

Recent research endeavours have theoretically shown the beneficial effect of cooperation in multi-agent re-inforcement 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 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 AsyncMATD, for which we establish a linear convergence speedup while highlighting the effect of time-varying asynchronous delays on the resulting convergence rate.