TY - JOUR

T1 - Guarantees for Epsilon-Greedy Reinforcement Learning with Function Approximation

AU - Dann, Christoph

AU - Mansour, Yishay

AU - Mohri, Mehryar

AU - Sekhari, Ayush

AU - Sridharan, Karthik

N1 - Publisher Copyright:
Copyright © 2022 by the author(s)

PY - 2022

Y1 - 2022

N2 - Myopic exploration policies such as ε-greedy, softmax, or Gaussian noise fail to explore efficiently in some reinforcement learning tasks and yet, they perform well in many others. In fact, in practice, they are often selected as the top choices, due to their simplicity. But, for what tasks do such policies succeed? Can we give theoretical guarantees for their favorable performance? These crucial questions have been scarcely investigated, despite the prominent practical importance of these policies. This paper presents a theoretical analysis of such policies and provides the first regret and sample-complexity bounds for reinforcement learning with myopic exploration. Our results apply to value-function-based algorithms in episodic MDPs with bounded Bellman Eluder dimension. We propose a new complexity measure called myopic exploration gap, denoted by α, that captures a structural property of the MDP, the exploration policy expl and the given value function class F. We show that the sample-complexity of myopic exploration scales quadratically with the inverse of this quantity, 1/α2. We further demonstrate through concrete examples that myopic exploration gap is indeed favorable in several tasks where myopic exploration succeeds, due to the corresponding dynamics and reward structure.

AB - Myopic exploration policies such as ε-greedy, softmax, or Gaussian noise fail to explore efficiently in some reinforcement learning tasks and yet, they perform well in many others. In fact, in practice, they are often selected as the top choices, due to their simplicity. But, for what tasks do such policies succeed? Can we give theoretical guarantees for their favorable performance? These crucial questions have been scarcely investigated, despite the prominent practical importance of these policies. This paper presents a theoretical analysis of such policies and provides the first regret and sample-complexity bounds for reinforcement learning with myopic exploration. Our results apply to value-function-based algorithms in episodic MDPs with bounded Bellman Eluder dimension. We propose a new complexity measure called myopic exploration gap, denoted by α, that captures a structural property of the MDP, the exploration policy expl and the given value function class F. We show that the sample-complexity of myopic exploration scales quadratically with the inverse of this quantity, 1/α2. We further demonstrate through concrete examples that myopic exploration gap is indeed favorable in several tasks where myopic exploration succeeds, due to the corresponding dynamics and reward structure.

UR - http://www.scopus.com/inward/record.url?scp=85151685111&partnerID=8YFLogxK

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AN - SCOPUS:85151685111

SN - 2640-3498

VL - 162

SP - 4666

EP - 4689

JO - Proceedings of Machine Learning Research

JF - Proceedings of Machine Learning Research

T2 - 39th International Conference on Machine Learning, ICML 2022

Y2 - 17 July 2022 through 23 July 2022

ER -