The Sample Complexity of Policy Learning with Mu-Resets

Abstract

We study policy-based reinforcement learning under the $\mu$-resets interaction protocol of Kakade and Langford [KL02]. This interaction protocol enables the learner to sample trajectories from a given exploratory reset distribution $\mu$, in addition to the starting distribution. We resolve the question raised by [KLS25] on the role of policy realizability for the sample complexity of this problem. Critically, the dependence on horizon $H$ is governed by the notion of coverage assumed of the reset distribution. Under bounded all-policy concentrability, we show a $\exp(\Omega(H))$ sample complexity lower bound; with bounded pushforward concentrability, we show the dependence on horizon is tightly characterized as $\exp(\Theta(\sqrt H))$.