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Fast Convergence of Softmax Policy Mirror Ascent for Bandits & Tabular MDPs

Résumé

We analyze the convergence of a novel policy gradient algorithm (referred to as SPMA) for multi-armed bandits and tabular Markov decision processes (MDPs). SPMA is an instantiation of mirror ascent and uses the softmax parameterization with a log-sum-exp mirror map. Given access to the exact policy gradients, we prove that SPMA with a constant step-size requires iterations to converge to an -optimal policy. The resulting convergence rate is better than both the

rate for constant step-size softmax policy gradient (SPG) and the

rate for SPG with Nesterov acceleration. Furthermore, unlike the SPG results, the convergence rate for SPMA does not depend on potentially large problem-dependent constants, and matches the rate achieved by natural policy gradient (NPG). Furthermore, for multi-armed bandits, we prove that SPMA with gap-dependent step-sizes can result in global super-linear convergence. Our experimental evaluations on tabular MDPs and continuous control tasks demonstrate that SPMA consistently outperforms SPG while achieving similar or better performance compared to NPG.

Publication
Workshop at the Neural Information Processing Systems (NeurIPS)
Issam H. Laradji
Issam H. Laradji
Research Manager

Research Manager at AI Frontier Research located at Vancouver, BC, Canada.