Implicit Finite-Horizon Approximation and Efficient Optimal Algorithms for Stochastic Shortest Path

TL;DR

This paper presents a new analysis technique called implicit finite-horizon approximation for developing minimax optimal regret algorithms in the Stochastic Shortest Path model, resulting in more efficient and adaptable algorithms.

Contribution

It introduces a novel analysis method and develops the first model-free minimax optimal SSP algorithm, along with an improved model-based algorithm with sparse updates.

Findings

First model-free minimax optimal SSP algorithm.

Sparse update algorithms improve computational efficiency.

Algorithms are adaptable and can be parameter-free.

Abstract

We introduce a generic template for developing regret minimization algorithms in the Stochastic Shortest Path (SSP) model, which achieves minimax optimal regret as long as certain properties are ensured. The key of our analysis is a new technique called implicit finite-horizon approximation, which approximates the SSP model by a finite-horizon counterpart only in the analysis without explicit implementation. Using this template, we develop two new algorithms: the first one is model-free (the first in the literature to our knowledge) and minimax optimal under strictly positive costs; the second one is model-based and minimax optimal even with zero-cost state-action pairs, matching the best existing result from [Tarbouriech et al., 2021b]. Importantly, both algorithms admit highly sparse updates, making them computationally more efficient than all existing algorithms. Moreover, both can be made completely parameter-free.