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# A Unified Algorithm for Stochastic Path Problems

*Proceedings of The 34th International Conference on Algorithmic Learning Theory*, PMLR 201:510-557, 2023.

#### Abstract

We study reinforcement learning in stochastic path (SP) problems. The goal in these problems is to maximize the expected sum of rewards until the agent reaches a terminal state. We provide the first regret guarantees in this general problem by analyzing a simple optimistic algorithm. Our regret bound matches the best known results for the well-studied special case of stochastic shortest path (SSP) with all non-positive rewards. For SSP, we present an adaptation procedure for the case when the scale of rewards $B_\star$ is unknown. We show that there is no price for adaptation, and our regret bound matches that with a known $B_\star$. We also provide a scale adaptation procedure for the special case of stochastic longest paths (SLP) where all rewards are non-negative. However, unlike in SSP, we show through a lower bound that there is an unavoidable price for adaptation.