Trajectory Data Suffices for Statistically Efficient Policy Evaluation in Fixed-Horizon Offline RL with Linear q^π-Realizability and Concentrability

We study fixed-horizon offline reinforcement learning (RL) with function approximation for both policy evaluation and policy optimization. Prior work established that statistically efficient learning is impossible for either of these problems when the only assumptions are that the data has good coverage (concentrability) and the state-action value function of every policy is linearly realizable ($q^\pi$-realizability) [Foster et al., 2022]. Recently, Tkachuk et al. [2024] gave a statistically efficient learner for policy optimization, if in addition the data is assumed to be given as trajectories. In this work we present a statistically efficient learner for policy evaluation under the same assumptions, with the additional requirement that the behavior policy is known. Further, we show that the sample complexity of the learner used by Tkachuk et al. [2024] for policy optimization can be improved by a tighter analysis.