In offline reinforcement learning (RL), a learner leverages prior logged data to learn a good policy without interacting with the environment. A major challenge in applying such methods in practice is the lack of both theoretically principled and practical tools for model selection and evaluation. To address this, we study the problem of model selection in offline RL with value function approximation. The learner is given a nested sequence of model classes to minimize squared Bellman error and must select among these to achieve a balance between approximation and estimation error of the classes. We propose the first model selection algorithm for offline RL that achieves minimax rate-optimal oracle inequalities up to logarithmic factors. The algorithm, MODBE, takes as input a collection of candidate model classes and a generic base offline RL algorithm. By successively eliminating model classes using a novel one-sided generalization test, MODBE returns a policy with regret scaling with the complexity of the minimally complete model class. In addition to its theoretical guarantees, it is conceptually simple and computationally efficient, amounting to solving a series of square loss regression problems and then comparing relative square loss between classes. We conclude with several numerical simulations showing it ismore »
This content will become publicly available on April 1, 2023
Bellman Residual Orthogonalization for Offline Reinforcement Learning
We propose and analyze a reinforcement learning principle that
approximates the Bellman equations by enforcing their validity only
along an user-defined space of test functions. Focusing on
applications to model-free offline RL with function approximation, we
exploit this principle to derive confidence intervals for off-policy
evaluation, as well as to optimize over policies within a prescribed
policy class. We prove an oracle inequality on our policy optimization
procedure in terms of a trade-off between the value and uncertainty of
an arbitrary comparator policy. Different choices of test function
spaces allow us to tackle different problems within a common
framework. We characterize the loss of efficiency in moving from
on-policy to off-policy data using our procedures, and establish
connections to concentrability coefficients studied in past work. We
examine in depth the implementation of our methods with linear
function approximation, and provide theoretical guarantees with
polynomial-time implementations even when Bellman closure does not
hold.
- Publication Date:
- NSF-PAR ID:
- 10343719
- Journal Name:
- ArXivorg
- ISSN:
- 2331-8422
- Sponsoring Org:
- National Science Foundation
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