Oracle Inequalities for Model Selection in Offline Reinforcement Learning

TL;DR

This paper introduces ModBE, a new model selection algorithm for offline reinforcement learning that achieves near-optimal theoretical guarantees and effectively balances approximation and estimation errors.

Contribution

The paper presents the first minimax rate-optimal model selection algorithm for offline RL with value function approximation, using a novel elimination method.

Findings

ModBE achieves minimax rate-optimal oracle inequalities.

The algorithm is simple, computationally efficient, and relies on square loss regression.

Numerical simulations demonstrate effective model class selection.

Abstract

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 is capable of reliably selecting a good model class.