Offline Stochastic Shortest Path: Learning, Evaluation and Towards Optimality

TL;DR

This paper investigates the offline stochastic shortest path problem in finite state and action spaces, proposing simple algorithms with strong theoretical guarantees for policy evaluation and learning.

Contribution

It introduces value iteration-based algorithms for offline SSP and provides instance-dependent bounds that approach near-minimax optimality.

Findings

Algorithms achieve strong statistical guarantees

Instance-dependent bounds are near-minimax optimal

Study illuminates fundamental limits of offline SSP

Abstract

Goal-oriented Reinforcement Learning, where the agent needs to reach the goal state while simultaneously minimizing the cost, has received significant attention in real-world applications. Its theoretical formulation, stochastic shortest path (SSP), has been intensively researched in the online setting. Nevertheless, it remains understudied when such an online interaction is prohibited and only historical data is provided. In this paper, we consider the offline stochastic shortest path problem when the state space and the action space are finite. We design the simple value iteration-based algorithms for tackling both offline policy evaluation (OPE) and offline policy learning tasks. Notably, our analysis of these simple algorithms yields strong instance-dependent bounds which can imply worst-case bounds that are near-minimax optimal. We hope our study could help illuminate the fundamental statistical limits of the offline SSP problem and motivate further studies beyond the scope of current consideration.