Shortest-Path Constrained Reinforcement Learning for Sparse Reward Tasks

TL;DR

This paper introduces the k-Shortest-Path (k-SP) constraint to improve sample efficiency in sparse reward reinforcement learning by restricting trajectory exploration, combined with a penalty-based approach to maintain exploration diversity.

Contribution

It proposes a novel k-SP constraint for RL that enhances sample efficiency and introduces a penalty-based method to balance exploration and exploitation.

Findings

Significantly reduces trajectory space in tabular RL.

Improves sample efficiency in continuous control tasks.

Outperforms existing exploration methods like count-based exploration.

Abstract

We propose the k-Shortest-Path (k-SP) constraint: a novel constraint on the agent's trajectory that improves the sample efficiency in sparse-reward MDPs. We show that any optimal policy necessarily satisfies the k-SP constraint. Notably, the k-SP constraint prevents the policy from exploring state-action pairs along the non-k-SP trajectories (e.g., going back and forth). However, in practice, excluding state-action pairs may hinder the convergence of RL algorithms. To overcome this, we propose a novel cost function that penalizes the policy violating SP constraint, instead of completely excluding it. Our numerical experiment in a tabular RL setting demonstrates that the SP constraint can significantly reduce the trajectory space of policy. As a result, our constraint enables more sample efficient learning by suppressing redundant exploration and exploitation. Our experiments on MiniGrid, DeepMind Lab, Atari, and Fetch show that the proposed method significantly improves proximal policy optimization (PPO) and outperforms existing novelty-seeking exploration methods including count-based exploration even in continuous control tasks, indicating that it improves the sample efficiency by preventing the agent from taking redundant actions.