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

We study reward-free reinforcement learning (RL) under general non-linear function approximation, and establish sample efficiency and hardness results under various standard structural assumptions. On the positive side, we propose the RFOLIVE (Reward-Free OLIVE) algorithm for sample-efficient reward-free exploration under minimal structural assumptions, which covers the previously studied settings of linear MDPs (Jin et al., 2020b), linear completeness (Zanette et al., 2020b) and low-rank MDPs with unknown representation (Modi et al., 2021). Our analyses indicate that the explorability or reachability assumptions, previously made for the latter two settings, are not necessary statistically for reward-free exploration. On the negative side, we provide a statistical hardness result for both reward-free and reward-aware exploration under linear completeness assumptions when the underlying features are unknown, showing an exponential separation between low-rank and linear completeness settings. * Equal contribution 36th Conference on Neural Information Processing Systems (NeurIPS 2022). rank MDP settings require explorability/reachability assumptions (Zanette et al., 2020b; Modi et al., 2021), which, roughly speaking, assert that every direction in the state-action feature space can be visited with sufficient probability. These assumptions are often not needed in reward-aware RL but suspected to be necessary for model-free reward-free settings. Our results do not depend on such assumptions, showing that they are not necessary for sample-efficient reward-free exploration either. Implications: negative results We develop lower bounds, showing that some of the structural assumptions made here are not easily relaxed further. While the settings of linear completeness with known features (Row 3), and low-rank MDPs with unknown features (Row 4) are both independently tractable, we show a hardness result against learning under linear completeness when the features are unknown, even under a few additional assumptions (Row 6). Taken together, our results take a significant step in bridging the sizeable gap in our understanding of reward-aware and reward-free settings and bring the two closer to an equal footing. Related work In recent years, we have seen a wide range of results for reward-aware RL under general function approximation (