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# Finite-Time Analysis of Asynchronous Stochastic Approximation and $Q$-Learning

*Proceedings of Thirty Third Conference on Learning Theory*, PMLR 125:3185-3205, 2020.

#### Abstract

We consider a general asynchronous Stochastic Approximation (SA) scheme featuring a weighted infinity-norm contractive operator, and prove a bound on its finite-time convergence rate on a single trajectory. Additionally, we specialize the result to asynchronous $Q$-learning. The resulting bound matches the sharpest available bound for synchronous $Q$-learning, and improves over previous known bounds for asynchronous $Q$-learning.