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Non-stationarity is a fundamental challenge in multi-agent reinforcementlearning (MARL), where agents update their behaviour as they learn. Manytheoretical advances in MARL avoid the challenge of non-stationarity bycoordinating the policy updates of agents in various ways, includingsynchronizing times at which agents are allowed to revise their policies.Synchronization enables analysis of many MARL algorithms via multi-timescalemethods, but such synchrony is infeasible in many decentralized applications.In this paper, we study an asynchronous variant of the decentralized Q-learningalgorithm, a recent MARL algorithm for stochastic games. We provide sufficientconditions under which the asynchronous algorithm drives play to equilibriumwith high probability. Our solution utilizes constant learning rates in theQ-factor update, which we show to be critical for relaxing the synchronyassumptions of earlier work. Our analysis also applies to asynchronousgeneralizations of a number of other algorithms from the regret testingtradition, whose performance is analyzed by multi-timescale methods that studyMarkov chains obtained via policy update dynamics. This work extends theapplicability of the decentralized Q-learning algorithm and its relatives tosettings in which parameters are selected in an independent manner, and tamesnon-stationarity without imposing the coordination assumptions of prior work.

Asynchronous Decentralized Q-Learning: Two Timescale Analysis By Persistence