On The Statistical Complexity of Offline Decision-Making

TL;DR

This paper investigates the fundamental limits of offline decision-making with function approximation, providing near-optimal rates for stochastic contextual bandits and MDPs, and introducing a new data coverage measure.

Contribution

It establishes minimax-optimal rates based on pseudo-dimension and introduces a novel characterization of behavior policy that generalizes previous data coverage notions.

Findings

Derived near-minimax rates for offline decision-making tasks.

Introduced a new measure of data coverage that subsumes previous notions.

Showed benefits of offline data in online decision-making regimes.

Abstract

We study the statistical complexity of offline decision-making with function approximation, establishing (near) minimax-optimal rates for stochastic contextual bandits and Markov decision processes. The performance limits are captured by the pseudo-dimension of the (value) function class and a new characterization of the behavior policy that \emph{strictly} subsumes all the previous notions of data coverage in the offline decision-making literature. In addition, we seek to understand the benefits of using offline data in online decision-making and show nearly minimax-optimal rates in a wide range of regimes.