Policy Learning with Observational Data (1702.02896v6)

Abstract: In many areas, practitioners seek to use observational data to learn a treatment assignment policy that satisfies application-specific constraints, such as budget, fairness, simplicity, or other functional form constraints. For example, policies may be restricted to take the form of decision trees based on a limited set of easily observable individual characteristics. We propose a new approach to this problem motivated by the theory of semiparametrically efficient estimation. Our method can be used to optimize either binary treatments or infinitesimal nudges to continuous treatments, and can leverage observational data where causal effects are identified using a variety of strategies, including selection on observables and instrumental variables. Given a doubly robust estimator of the causal effect of assigning everyone to treatment, we develop an algorithm for choosing whom to treat, and establish strong guarantees for the asymptotic utilitarian regret of the resulting policy.

• The paper's main contribution is integrating semiparametric efficiency and doubly robust estimation to reliably optimize treatment assignment policies.
• The methodology addresses both binary and continuous treatments through local linear approximations and instrumental variable strategies for causal inference.
• Empirical results from simulations and real-world datasets validate minimax regret guarantees and robust policy convergence under practical constraints.

Policy Learning with Observational Data

The paper "Policy Learning with Observational Data" by Susan Athey and Stefan Wager presents a robust framework for deriving treatment assignment policies from observational data, respecting critical constraints such as budget, fairness, and simplicity. Their methodological contribution stems from the infusion of semiparametric efficiency theory, allowing optimization over both binary treatments and mechanisms involving infinitesimally small changes in continuous treatments. A cornerstone of the approach is the use of doubly robust estimation, which provides resilience against certain types of model specification errors and enhances causal effect estimation from observational data.

Overview

The authors propose an algorithm designed to learn treatment assignment policies utilizing observational data with the intent to optimize a specific application-based utility function, subjected to predefined constraints. Central to their approach is the use of doubly robust estimators for causal effects, where these estimators are formed through a combination of selection on observables and instrumental variable strategies. Their method includes policy learning within binary treatments as well as the continuous treatment framework, where policies are refined using local linear approximations to derive "nudges" instead of global shifts.

Methodological Advances

The paper advances policy learning by incorporating semiparametric efficiency principles into the estimation framework. This integration allows for consistent policy optimization and robust performance under various sampling designs:

• Doubly Robust Estimation: The authors utilize doubly robust scores to estimate treatment effects reliably. These scores possess the appealing property of remaining consistent if either the model for the potential outcomes or the model for the treatment assignment is correctly specified, not necessarily both.
• Asymptotic Guarantees and Minimax Regret: The paper establishes asymptotic results linking the performance of policy choices to Vapnik-Chervonenkis (VC) bounds on complexity, offering minimax regret guarantees. They demonstrate that policies derived using their method converge to optimality at the rate of $\sqrt{\text{VC}(\Pi) / n}$, with $\Pi$ being the policy class and $n$ the number of observations.

Empirical Results

The authors provide empirical insights by testing their framework on simulated data and real-world datasets, showcasing the efficacy of their approach in various scenarios such as policy learning in economic interventions and targeted marketing. Notably, their approach achieves strong numerical results in simulations involving imperfect compliance and endogenous selection, managed through instrumental variable techniques.

Implications and Future Work

This research has significant implications for domains reliant on causal inference from observational datasets. The approach is versatile enough to accommodate constraints typical in medical treatment allocations, educational program rollouts, and many other fields where decisions must harmonize efficacy, fairness, and budgetary limits. By mitigating biases inherent in observational analyses, the frameworks enhance real-world policy formulation under uncertainty.

Looking forward, the authors identify realms for additional exploration and refinement, including:

• Dynamic Policies: Extending the framework to adaptively learn policies in sequential decision-making contexts.
• Nonparametric Complexity: Further reducing complexity by utilizing emerging machine learning methods to better approximate conditional expectations without stringent reliance on parametric forms.

In conclusion, Athey and Wager offer a sophisticated template for extracting actionable policies from complex, noisy observational datasets. This work opens avenues for more robust and fair policy deployments, serving as a crucial bridge between theoretical econometrics and applicable data-driven decision making.