DASA: Delay-Adaptive Multi-Agent Stochastic Approximation

We consider a setting in which $N$ agents aim to speedup a common Stochastic Approximation (SA) problem by acting in parallel and communicating with a central server. We assume that the up-link transmissions to the server are subject to asynchronous and potentially unbounded time-varying delays. To mitigate the effect of delays and stragglers while reaping the benefits of distributed computation, we propose $\mathtt{\text{DASA}}$, a Delay-Adaptive algorithm for multi-agent Stochastic Approximation. We provide a finite-time analysis of $\mathtt{\text{DASA}}$ assuming that the agents’ stochastic observation processes are independent Markov chains. Significantly advancing existing results, $\mathtt{\text{DASA}}$ is the first algorithm whose convergence rate depends only on the mixing time ${\tau }_{mix}$ and on the average delay ${\tau }_{avg}$ while jointly achieving an $N$-fold convergence speedup under Markovian sampling. Our work is relevant for various SA applications, including multi-agent and distributed temporal difference (TD) learning, Q-learning and stochastic optimization with correlated data.