  Offline (or batch) reinforcement learning (RL) algorithms seek to learn an
optimal policy from a fixed dataset without active data collection. Based on
the composition of the offline dataset, two main categories of methods are
used: imitation learning which is suitable for expert datasets and vanilla
offline RL which often requires uniform coverage datasets. From a practical
standpoint, datasets often deviate from these two extremes and the exact data
composition is usually unknown a priori. To bridge this gap, we present a new
offline RL framework that smoothly interpolates between the two extremes of
data composition, hence unifying imitation learning and vanilla offline RL. The
new framework is centered around a weak version of the concentrability
coefficient that measures the deviation from the behavior policy to the expert
policy alone.
  Under this new framework, we further investigate the question on algorithm
design: can one develop an algorithm that achieves a minimax optimal rate and
also adapts to unknown data composition? To address this question, we consider
a lower confidence bound (LCB) algorithm developed based on pessimism in the
face of uncertainty in offline RL. We study finite-sample properties of LCB as
well as information-theoretic limits in multi-armed bandits, contextual
bandits, and Markov decision processes (MDPs). Our analysis reveals surprising
facts about optimality rates. In particular, in all three settings, LCB
achieves a faster rate of $1/N$ for nearly-expert datasets compared to the
usual rate of $1/\sqrt{N}$ in offline RL, where $N$ is the number of samples in
the batch dataset. In the case of contextual bandits with at least two
contexts, we prove that LCB is adaptively optimal for the entire data
composition range, achieving a smooth transition from imitation learning to
offline RL. We further show that LCB is almost adaptively optimal in MDPs.
