There has been considerable interest across several fields in methods that reduce the problem of learning good treatment assignment policies to the problem of accurate policy evaluation. Given a class of candidate policies, these methods first effectively evaluate each policy individually, and then learn a policy by optimizing the estimated value function; such approaches are guaranteed to be risk-consistent whenever the policy value estimates are uniformly consistent . However, despite the wealth of proposed methods, the literature remains largely silent on questions of statistical efficiency: there are only limited results characterizing which policy evaluation strategies lead to better learned policies than others, or what the optimal policy evaluation strategies are . In this paper, we build on classical results in semiparametric efficiency theory to develop quasi-optimal methods for policy learning; in particular, we propose a class of policy value estimators that, when optimized, yield regret bounds for the learned policy that scale with the semiparametric efficient variance for policy evaluation. On a practical level, our result suggests new methods for policy learning motivated by semiparametric efficiency theory .
We consider the problem of using observational data to learn treatment assignment policies that satisfy certain constraints specified 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 .
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There has been considerable interest across several fields in methods that reduce
We consider
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learning good
using observational data to learn
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to the problem of accurate policy evaluation. Given a class of candidate policies, these methods first effectively evaluate each policy individually, and then learn a policy by optimizing the estimated value function; such approaches are guaranteed to be risk-consistent whenever the policy value estimates are uniformly consistent
that satisfy certain constraints specified 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
R
despite the wealth of proposed methods, the literature remains largely silent on questions of statistical efficiency: there are only limited results characterizing which policy evaluation strategies lead to better learned policies than others, or what the optimal policy evaluation strategies are
several key analytical components are missing, including a characterization of optimal methods for policy learning, and sharp bounds for minimax regret
R
build on classical results in semiparametric efficiency theory to develop quasi-optimal methods for policy learning; in particular, we propose a class of policy value estimators that, when optimized, yield regret bounds for the learned policy that scale with the semiparametric efficient variance for policy evaluation. On a practical level, our result suggests new methods for policy learning motivated by semiparametric efficiency theory
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