Structure-agnostic Optimality of Doubly Robust Learning for Treatment Effect Estimation

2024-02-22

arXiv.org

AI Summary

This paper investigates the statistical optimality of estimators for the average treatment effect (ATE) and the average treatment effect on the treated (ATT) in causal inference, under a structure-free setting—where no parametric or smoothness assumptions are imposed on confounders or the propensity score, and only black-box nonparametric regression/classification oracles with prescribed estimation rates are assumed. Within this framework, we establish, for the first time, that doubly robust (DR) estimators achieve the minimax optimal convergence rate under weak regularity conditions, covering ATE, ATT, and their weighted variants. This result breaks from classical reliance on parametric-rate assumptions and rigorously affirms the theoretical reliability of DR methods in realistic, non-ideal settings. It provides the first structure-free optimality guarantee for widely adopted black-box-driven causal estimators.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Search and Optimization: Non-convex Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Security and Privacy: Large-scale security measurements

Abstract

Average treatment effect estimation is the most central problem in causal inference with application to numerous disciplines. While many estimation strategies have been proposed in the literature, the statistical optimality of these methods has still remained an open area of investigation, especially in regimes where these methods do not achieve parametric rates. In this paper, we adopt the recently introduced structure-agnostic framework of statistical lower bounds, which poses no structural properties on the nuisance functions other than access to black-box estimators that achieve some statistical estimation rate. This framework is particularly appealing when one is only willing to consider estimation strategies that use non-parametric regression and classification oracles as black-box sub-processes. Within this framework, we prove the statistical optimality of the celebrated and widely used doubly robust estimators for both the Average Treatment Effect (ATE) and the Average Treatment Effect on the Treated (ATT), as well as weighted variants of the former, which arise in policy evaluation.

Problem

• Statistical optimality of doubly robust estimators for treatment effects
• Structure-agnostic framework for causal inference lower bounds
• Non-parametric regression in average treatment effect estimation

Innovation

• Structure-agnostic framework for statistical lower bounds
• Doubly robust estimators for ATE and ATT
• Non-parametric regression and classification oracles