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.
@article{arxiv.2002.00260,
title = {Finite-Time Analysis of Asynchronous Stochastic Approximation and $Q$-Learning},
author = {Guannan Qu and Adam Wierman},
journal= {arXiv preprint arXiv:2002.00260},
year = {2020}
}