Minimax-Optimal Reward-Agnostic Exploration in Reinforcement Learning
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This paper studies reward-agnostic exploration in reinforcement learning (RL) – a scenario where the learner is unware of the reward functions during the exploration stage – and designs an algorithm that improves over the state of the art. More precisely, consider a finite-horizon non-stationary Markov decision process with S states, A actions, and horizon length H, and suppose that there are no more than a polynomial number of given reward functions of interest. By collecting an order of SAH^3/ε^2 sample episodes (up to log factor) without guidance of the reward information, our algorithm is able to find ε-optimal policies for all these reward functions, provided that ε is sufficiently small. This forms the first reward-agnostic exploration scheme in this context that achieves provable minimax optimality. Furthermore, once the sample size exceeds S^2AH^3/ε^2 episodes (up to log factor), our algorithm is able to yield ε accuracy for arbitrarily many reward functions (even when they are adversarially designed), a task commonly dubbed as “reward-free exploration.” The novelty of our algorithm design draws on insights from offline RL: the exploration scheme attempts to maximize a critical reward-agnostic quantity that dictates the performance of offline RL, while the policy learning paradigm leverages ideas from sample-optimal offline RL paradigms.
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