  Off-policy evaluation (OPE) in reinforcement learning allows one to evaluate
novel decision policies without needing to conduct exploration, which is often
costly or otherwise infeasible. We consider for the first time the
semiparametric efficiency limits of OPE in Markov decision processes (MDPs),
where actions, rewards, and states are memoryless. We show existing OPE
estimators may fail to be efficient in this setting. We develop a new estimator
based on cross-fold estimation of $q$-functions and marginalized density
ratios, which we term double reinforcement learning (DRL). We show that DRL is
efficient when both components are estimated at fourth-root rates and is also
doubly robust when only one component is consistent. We investigate these
properties empirically and demonstrate the performance benefits due to
harnessing memorylessness.
