{\epsilon}-BMC: A Bayesian Ensemble Approach to Epsilon-Greedy Exploration in Model-Free Reinforcement Learning

TL;DR

This paper introduces a Bayesian ensemble method for dynamically adapting epsilon in epsilon-greedy exploration, improving exploration efficiency in model-free reinforcement learning.

Contribution

It presents a novel Bayesian perspective on epsilon as a measure of Q-value uniformity and develops a closed-form Bayesian update for adaptive epsilon tuning.

Findings

Efficiently balances exploration and exploitation across various problems.

Outperforms fixed schedules and existing adaptive schemes.

Provides monotone convergence guarantees.

Abstract

Resolving the exploration-exploitation trade-off remains a fundamental problem in the design and implementation of reinforcement learning (RL) algorithms. In this paper, we focus on model-free RL using the epsilon-greedy exploration policy, which despite its simplicity, remains one of the most frequently used forms of exploration. However, a key limitation of this policy is the specification of $\varepsilon$. In this paper, we provide a novel Bayesian perspective of $\varepsilon$ as a measure of the uniformity of the Q-value function. We introduce a closed-form Bayesian model update based on Bayesian model combination (BMC), based on this new perspective, which allows us to adapt $\varepsilon$ using experiences from the environment in constant time with monotone convergence guarantees. We demonstrate that our proposed algorithm, $\varepsilon$-\texttt{BMC}, efficiently balances exploration and exploitation on different problems, performing comparably or outperforming the best tuned fixed annealing schedules and an alternative data-dependent $\varepsilon$ adaptation scheme proposed in the literature.