Policy Optimization for Stochastic Shortest Path

TL;DR

This paper introduces a novel policy optimization approach for stochastic shortest path problems, providing near-optimal regret bounds across various settings and proposing a new approximation scheme that improves learning efficiency.

Contribution

It develops a new stacked discounted approximation scheme and extends policy optimization to SSP, achieving near-optimal regret bounds in diverse environments.

Findings

Achieves near-optimal regret bounds in multiple SSP settings.

Introduces a new approximation scheme called stacked discounted approximation.

Enables learning near-stationary policies with minimal changes during episodes.

Abstract

Policy optimization is among the most popular and successful reinforcement learning algorithms, and there is increasing interest in understanding its theoretical guarantees. In this work, we initiate the study of policy optimization for the stochastic shortest path (SSP) problem, a goal-oriented reinforcement learning model that strictly generalizes the finite-horizon model and better captures many applications. We consider a wide range of settings, including stochastic and adversarial environments under full information or bandit feedback, and propose a policy optimization algorithm for each setting that makes use of novel correction terms and/or variants of dilated bonuses (Luo et al., 2021). For most settings, our algorithm is shown to achieve a near-optimal regret bound. One key technical contribution of this work is a new approximation scheme to tackle SSP problems that we call \textit{stacked discounted approximation} and use in all our proposed algorithms. Unlike the finite-horizon approximation that is heavily used in recent SSP algorithms, our new approximation enables us to learn a near-stationary policy with only logarithmic changes during an episode and could lead to an exponential improvement in space complexity.