Bellman Residual Orthogonalization for Offline Reinforcement Learning
This work addresses the challenge of reliable policy optimization and evaluation in offline RL settings, offering a flexible framework that is incremental but with strong theoretical underpinnings for practical applications.
The paper tackles the problem of offline reinforcement learning with function approximation by proposing a principle that approximates Bellman equations using user-defined test functions, enabling confidence intervals for off-policy evaluation and policy optimization with proven oracle inequalities. It provides theoretical guarantees for polynomial-time implementations even without Bellman closure, characterizing efficiency loss in terms of concentrability coefficients.
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.