  Several recent works have proposed a class of algorithms for the offline
reinforcement learning (RL) problem that we will refer to as return-conditioned
supervised learning (RCSL). RCSL algorithms learn the distribution of actions
conditioned on both the state and the return of the trajectory. Then they
define a policy by conditioning on achieving high return. In this paper, we
provide a rigorous study of the capabilities and limitations of RCSL, something
which is crucially missing in previous work. We find that RCSL returns the
optimal policy under a set of assumptions that are stronger than those needed
for the more traditional dynamic programming-based algorithms. We provide
specific examples of MDPs and datasets that illustrate the necessity of these
assumptions and the limits of RCSL. Finally, we present empirical evidence that
these limitations will also cause issues in practice by providing illustrative
experiments in simple point-mass environments and on datasets from the D4RL
benchmark.
