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We study reward-free reinforcement learning (RL) under general non-linearfunction approximation, and establish sample efficiency and hardness resultsunder various standard structural assumptions. On the positive side, we proposethe RFOLIVE (Reward-Free OLIVE) algorithm for sample-efficient reward-freeexploration under minimal structural assumptions, which covers the previouslystudied settings of linear MDPs (Jin et al., 2020b), linear completeness(Zanette et al., 2020b) and low-rank MDPs with unknown representation (Modi etal., 2021). Our analyses indicate that the explorability or reachabilityassumptions, previously made for the latter two settings, are not necessarystatistically for reward-free exploration. On the negative side, we provide astatistical hardness result for both reward-free and reward-aware explorationunder linear completeness assumptions when the underlying features are unknown,showing an exponential separation between low-rank and linear completenesssettings.

On the Statistical Efficiency of Reward-Free Exploration in Non-Linear RL