Planning in Hierarchical Reinforcement Learning: Guarantees for Using Local Policies

TL;DR

This paper develops theoretical guarantees for assembling local policies in hierarchical reinforcement learning, framing the problem as a traveling salesman problem with guarantees for stochastic policies in deterministic MDPs.

Contribution

It introduces three local stochastic policies with proven worst-case performance guarantees, advancing the understanding of policy assembly in hierarchical RL.

Findings

Stochastic policies outperform deterministic ones in worst-case scenarios.

Experimental results show stochastic policies perform better on average.

The approach applies to deterministic MDPs with collectible rewards.

Abstract

We consider a settings of hierarchical reinforcement learning, in which the reward is a sum of components. For each component we are given a policy that maximizes it and our goal is to assemble a policy from the individual policies that maximizes the sum of the components. We provide theoretical guarantees for assembling such policies in deterministic MDPs with collectible rewards. Our approach builds on formulating this problem as a traveling salesman problem with discounted reward. We focus on local solutions, i.e., policies that only use information from the current state; thus, they are easy to implement and do not require substantial computational resources. We propose three local stochastic policies and prove that they guarantee better performance than any deterministic local policy in the worst case; experimental results suggest that they also perform better on average.