Sufficient Decision Proxies for Decision-Focused Learning

TL;DR

This paper explores when and how different decision proxies can be effectively used in decision-focused learning to improve decision quality under uncertainty, proposing new proxies with minimal added complexity.

Contribution

It introduces problem property-based criteria for selecting decision proxies in DFL and presents alternative proxies that maintain learning simplicity.

Findings

Proposed decision proxies are effective across various problem types.

Certain problem properties justify the use of specific decision proxies.

Experimental results show improved decision quality with new proxies.

Abstract

When solving optimization problems under uncertainty with contextual data, utilizing machine learning to predict the uncertain parameters' values is a popular and effective approach. Decision-focused learning (DFL) aims at learning a predictive model such that decision quality, instead of prediction accuracy, is maximized. Common practice is to predict a single scenario representing the uncertain parameters, implicitly assuming that there exists a deterministic problem approximation (proxy) that allows for optimal decision-making. The opposite has also been considered, where the underlying distribution is estimated with a parameterized distribution. However, little is known about when either choice is valid. This paper investigates for the first time problem properties that justify using a certain decision proxy. Using this, we present alternative decision proxies for DFL, with little or no compromise on the complexity of the learning task. We show the effectiveness of presented approaches in experiments on continuous and discrete problems, as well as problems with uncertainty in the objective function and in the constraints.