Offline Multi-Action Policy Learning: Generalization and Optimization

TL;DR

This paper develops a theoretically optimal offline multi-action policy learning algorithm from observational data, addressing practical constraints like decision trees and budget limits, and demonstrating significant performance improvements.

Contribution

It introduces the first asymptotically minimax-optimal policy learning method for multi-action settings with observational data, including decision tree restrictions.

Findings

Achieves asymptotically minimax-optimal regret in multi-action policy learning.

Provides two computational approaches for decision tree policy implementation.

Demonstrates substantial performance improvements over existing algorithms.

Abstract

In many settings, a decision-maker wishes to learn a rule, or policy, that maps from observable characteristics of an individual to an action. Examples include selecting offers, prices, advertisements, or emails to send to consumers, as well as the problem of determining which medication to prescribe to a patient. While there is a growing body of literature devoted to this problem, most existing results are focused on the case where data comes from a randomized experiment, and further, there are only two possible actions, such as giving a drug to a patient or not. In this paper, we study the offline multi-action policy learning problem with observational data and where the policy may need to respect budget constraints or belong to a restricted policy class such as decision trees. We build on the theory of efficient semi-parametric inference in order to propose and implement a policy learning algorithm that achieves asymptotically minimax-optimal regret. To the best of our knowledge, this is the first result of this type in the multi-action setup, and it provides a substantial performance improvement over the existing learning algorithms. We then consider additional computational challenges that arise in implementing our method for the case where the policy is restricted to take the form of a decision tree. We propose two different approaches, one using a mixed integer program formulation and the other using a tree-search based algorithm.