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 \texttt{ DASA}, a Delay-Adaptive algorithm for multi-agent Stochastic Approximation. We provide a finite-time analysis of \texttt{ DASA} assuming that the agents' stochastic observation processes are independent Markov chains. Significantly advancing existing results, \texttt{ 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.
Categories: cs.AI cs.RO cs.SY eess.SY math.OC stat.ML