A Diffusion Analysis of Policy Gradient for Stochastic Bandits

Abstract

We study a continuous-time diffusion approximation of policy gradient for $k$-armed stochastic bandits. We prove that with a learning rate $\hat{I}\cdot =O(\hat{I}{”}^2/\log (n))$ the regret is $O(k\log (k)\log (n)/\hat{I}\cdot )$ where $n$ is the horizon and $\hat{I}”$ the minimum gap. Moreover, we construct an instance with only logarithmically many arms for which the regret is linear unless $\hat{I}\cdot =O(\hat{I}{”}^2)$.

17 pages