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Myopic exploration policies such as epsilon-greedy, softmax, or Gaussiannoise fail to explore efficiently in some reinforcement learning tasks and yet,they perform well in many others. In fact, in practice, they are often selectedas the top choices, due to their simplicity. But, for what tasks do suchpolicies succeed? Can we give theoretical guarantees for their favorableperformance? These crucial questions have been scarcely investigated, despitethe prominent practical importance of these policies. This paper presents atheoretical analysis of such policies and provides the first regret andsample-complexity bounds for reinforcement learning with myopic exploration.Our results apply to value-function-based algorithms in episodic MDPs withbounded Bellman Eluder dimension. We propose a new complexity measure calledmyopic exploration gap, denoted by alpha, that captures a structural propertyof the MDP, the exploration policy and the given value function class. We showthat the sample-complexity of myopic exploration scales quadratically with theinverse of this quantity, 1 / alpha^2. We further demonstrate through concreteexamples that myopic exploration gap is indeed favorable in several tasks wheremyopic exploration succeeds, due to the corresponding dynamics and rewardstructure.

Guarantees for Epsilon-Greedy Reinforcement Learning with Function Approximation