Near-Optimal Algorithms for Autonomous Exploration and Multi-Goal Stochastic Shortest Path

TL;DR

This paper introduces a new algorithm for autonomous exploration that achieves near-optimal sample complexity, along with a lower bound proof, connecting autonomous exploration to multi-goal stochastic shortest path problems.

Contribution

The paper presents a novel algorithm with improved sample complexity bounds and establishes the first lower bound for autonomous exploration, linking it to multi-goal stochastic shortest path.

Findings

Proposed algorithm is nearly minimax-optimal for polynomially growing $L$-controllable states.

Established the first lower bound for autonomous exploration.

Connected autonomous exploration to multi-goal stochastic shortest path problem.

Abstract

We revisit the incremental autonomous exploration problem proposed by Lim & Auer (2012). In this setting, the agent aims to learn a set of near-optimal goal-conditioned policies to reach the $L$-controllable states: states that are incrementally reachable from an initial state $s_0$ within $L$ steps in expectation. We introduce a new algorithm with stronger sample complexity bounds than existing ones. Furthermore, we also prove the first lower bound for the autonomous exploration problem. In particular, the lower bound implies that our proposed algorithm, Value-Aware Autonomous Exploration, is nearly minimax-optimal when the number of $L$-controllable states grows polynomially with respect to $L$. Key in our algorithm design is a connection between autonomous exploration and multi-goal stochastic shortest path, a new problem that naturally generalizes the classical stochastic shortest path problem. This new problem and its connection to autonomous exploration can be of independent interest.