Off-policy evaluation (OPE) in reinforcement learning is notoriously difficult in long- and infinite-horizon settings due to diminishing overlap between behavior and target policies. In this paper, we study the role of Markovian and time-invariant structure in efficient OPE. We first derive the efficiency bounds and efficient influence functions for OPE when one assumes each of these structures. This precisely characterizes the curse of horizon: in time-variant processes, OPE is only feasible in the near-on-policy setting, where behavior and target policies are sufficiently similar. But, in time-invariant Markov decision processes, our bounds show that truly off-policy evaluation is feasible, even with only just one dependent trajectory, and provide the limits of how well we could hope to do. We develop a new estimator based on double reinforcement learning (DRL) that leverages this structure for OPE. Our DRL estimator simultaneously uses estimated stationary density ratios and q-functions and remains efficient when both are estimated at slow, nonparametric rates and remains consistent when either is estimated consistently. We investigate these properties and the performance benefits of leveraging the problem structure for more efficient OPE.
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Double Reinforcement Learning for Efficient Off-Policy Evaluation in Markov Decision Processes
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.
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- Award ID(s):
- 1846210
- PAR ID:
- 10320788
- Date Published:
- Journal Name:
- Journal of machine learning research
- Volume:
- 21
- Issue:
- 167
- ISSN:
- 1532-4435
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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