Finite-Time Analysis of Asynchronous Stochastic Approximation and $Q$-Learning
; Proceedings of Thirty Third Conference on Learning Theory, PMLR 125:3185-3205, 2020.
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.