We consider the problem of using observational data to learn treatment assignment policies that satisfy certain constraintsspecified by a practitioner , such as budget, fairness, or functional form constraints. This problem has previously been studied in economics, statistics, and computer science, and several regret-consistent methods have been proposed. However, several key analytical components are missing, including a characterization of optimal methods for policy learning, and sharp bounds for minimax regret. In this paper, we derive lower bounds for the minimax regret of policy learning under constraints, and propose a method that attains this bound asymptotically up to a constant factor. Whenever the class of policies under consideration has a bounded Vapnik-Chervonenkis dimension, we show that the problem of minimax-regret policy learning can be asymptotically reduced to first efficiently evaluating how much each candidate policy improves over a randomized baseline, and then maximizing this value estimate. Our analysis relies on uniform generalizations of classical semiparametric efficiency results for average treatment effect estimation, paired with sharp concentration bounds for weighted empirical risk minimization that may be of independent interest .
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 limted set of easily observable individual characteristics. We propose a new approach to this problem motivated by the theory of semiparametrically efficient estimation. Our approach 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 .
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We consider the problem of using
In many areas, practitioners seek to use
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treatment assignment policies that satisfy certain constraintsspecified by a practitioner
a treatment assignment policy that satisfies application-specific constraints
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or
simplicity, or other
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This problem has previously been studied in economics, statistics, and computer science, and several regret-consistent methods have been proposed. However, several key analytical components are missing, including a characterization of optimal methods for policy learning, and sharp bounds for minimax regret. In this paper, we derive lower bounds for the minimax regret of policy learning under constraints, and propose a method that attains this bound asymptotically up to a constant factor. Whenever the class of policies under consideration has a bounded Vapnik-Chervonenkis dimension, we show that the problem of minimax-regret policy learning can be asymptotically reduced to first efficiently evaluating how much each candidate policy improves over a randomized baseline, and then maximizing this value estimate. Our analysis relies on uniform generalizations of classical semiparametric efficiency results for average treatment effect estimation, paired with sharp concentration bounds for weighted empirical risk minimization that may be of independent interest
For example, policies may be restricted to take the form of decision trees based on a limted set of easily observable individual characteristics. We propose a new approach to this problem motivated by the theory of semiparametrically efficient estimation. Our approach 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