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arXiv · 2007.10229

Regret Analysis of a Markov Policy Gradient Algorithm for Multi-arm Bandits

Denis Denisov·Neil Walton
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Abstract

We consider a policy gradient algorithm applied to a finite-arm bandit problem with Bernoulli rewards. We allow learning rates to depend on the current state of the algorithm, rather than use a deterministic time-decreasing learning rate. The state of the algorithm forms a Markov chain on the probability simplex. We apply Foster-Lyapunov techniques to analyse the stability of this Markov chain. We prove that if learning rates are well chosen then the policy gradient algorithm is a transient Markov chain and the state of the chain converges on the optimal arm with logarithmic or poly-logarithmic regret.

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BibTeXRIS

Denis Denisov, Neil Walton. 2020-07-20. Regret Analysis of a Markov Policy Gradient Algorithm for Multi-arm Bandits. https://arxiv.org/abs/2007.10229

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