Exploration in Reward Machines with Low Regret

Hippolyte Bourel, Anders Jonsson, Odalric-Ambrym Maillard, Mohammad Sadegh Talebi

Keywords: reward machine, regret minimization, non-markovian, temporal abstraction

TL;DR: We investigate reinforcement learning in average-reward Markov decision processes with reward machines in the regret minimization setting, and present regret a lower bound and two algorithms with provable regret bounds.

Abstract: We study reinforcement learning (RL) for decision processes with non-Markovian reward, in which high-level knowledge in the form of reward machines is available to the learner. Specifically, we investigate the efficiency of RL under the average-reward criterion, in the regret minimization setting. We propose two model-based RL algorithms that each exploits the structure of the reward machines, and show that our algorithms achieve regret bounds that improve over those of baselines by a multiplicative factor proportional to the number of states in the underlying reward machine. To the best of our knowledge, the proposed algorithms and associated regret bounds are the first to tailor the analysis specifically to reward machines, either in the episodic or average-reward settings. We also present a regret lower bound for the studied setting, which indicates that the proposed algorithms achieve a near-optimal regret. Finally, we report numerical experiments that demonstrate the superiority of the proposed algorithms over existing baselines in practice.