General Bayesian Policy Learning

TL;DR

This paper introduces the General Bayes framework for policy learning, using loss-based Bayesian updating and squared-loss surrogates to optimize decision rules with theoretical guarantees.

Contribution

It develops a novel Bayesian approach for policy learning that incorporates a squared-loss surrogate and provides theoretical PAC-Bayes guarantees.

Findings

Maximizes empirical welfare via a scaled squared error approach

Provides a Gaussian pseudo-likelihood interpretation of the generalized posterior

Demonstrates neural network implementation with theoretical guarantees

Abstract

This study proposes the General Bayes framework for policy learning. We consider decision problems in which a decision-maker chooses an action from an action set to maximize its expected welfare. Typical examples include treatment choice and portfolio selection. In such problems, the statistical target is a decision rule, and the prediction of each outcome $Y(a)$ is not necessarily of primary interest. We formulate this policy learning problem by loss-based Bayesian updating. Our main technical device is a squared-loss surrogate for welfare maximization. We show that maximizing empirical welfare over a policy class is equivalent to minimizing a scaled squared error in the outcome difference, up to a quadratic regularization controlled by a tuning parameter $\zeta>0$. This rewriting yields a General Bayes posterior over decision rules that admits a Gaussian pseudo-likelihood interpretation. We clarify two Bayesian interpretations of the resulting generalized posterior, a working Gaussian view and a decision-theoretic loss-based view. As one implementation example, we introduce neural networks with tanh-squashed outputs. Finally, we provide theoretical guarantees in a PAC-Bayes style.