Policy Mirror Descent Inherently Explores Action Space

TL;DR

This paper proves that online policy gradient methods can achieve optimal sample complexity without explicit exploration by introducing new evaluation operators and analysis techniques, improving efficiency and safety in reinforcement learning.

Contribution

The paper introduces two novel on-policy evaluation operators and a new analysis of stochastic policy mirror descent, enabling exploration-free policy gradient methods with optimal sample complexity.

Findings

Achieves $ ilde{O}(1/\epsilon^2)$ sample complexity without explicit exploration.

Introduces value-based estimation tailored to KL divergence.

Develops truncated on-policy Monte Carlo with strong convergence guarantees.

Abstract

Explicit exploration in the action space was assumed to be indispensable for online policy gradient methods to avoid a drastic degradation in sample complexity, for solving general reinforcement learning problems over finite state and action spaces. In this paper, we establish for the first time an $\tilde{\mathcal{O}}(1/\epsilon^2)$ sample complexity for online policy gradient methods without incorporating any exploration strategies. The essential development consists of two new on-policy evaluation operators and a novel analysis of the stochastic policy mirror descent method (SPMD). SPMD with the first evaluation operator, called value-based estimation, tailors to the Kullback-Leibler divergence. Provided the Markov chains on the state space of generated policies are uniformly mixing with non-diminishing minimal visitation measure, an $\tilde{\mathcal{O}}(1/\epsilon^2)$ sample complexity is obtained with a linear dependence on the size of the action space. SPMD with the second evaluation operator, namely truncated on-policy Monte Carlo (TOMC), attains an $\tilde{\mathcal{O}}(\mathcal{H}_{\mathcal{D}}/\epsilon^2)$ sample complexity, where $\mathcal{H}_{\mathcal{D}}$ mildly depends on the effective horizon and the size of the action space with properly chosen Bregman divergence (e.g., Tsallis divergence). SPMD with TOMC also exhibits stronger convergence properties in that it controls the optimality gap with high probability rather than in expectation. In contrast to explicit exploration, these new policy gradient methods can prevent repeatedly committing to potentially high-risk actions when searching for optimal policies.