End-to-end Conditional Robust Optimization

TL;DR

This paper introduces an end-to-end differentiable approach for Conditional Robust Optimization that improves decision-making under uncertainty by balancing empirical risk and conditional coverage, enhancing safety in high-stakes applications.

Contribution

It presents a novel training method combining differentiable optimization and logistic regression to improve conditional coverage and decision quality in CRO models.

Findings

Decisions trained with the proposed method outperform traditional approaches.

High-quality conditional coverage is empirically achieved.

The approach effectively balances risk and coverage in decision-making.

Abstract

The field of Contextual Optimization (CO) integrates machine learning and optimization to solve decision making problems under uncertainty. Recently, a risk sensitive variant of CO, known as Conditional Robust Optimization (CRO), combines uncertainty quantification with robust optimization in order to promote safety and reliability in high stake applications. Exploiting modern differentiable optimization methods, we propose a novel end-to-end approach to train a CRO model in a way that accounts for both the empirical risk of the prescribed decisions and the quality of conditional coverage of the contextual uncertainty set that supports them. While guarantees of success for the latter objective are impossible to obtain from the point of view of conformal prediction theory, high quality conditional coverage is achieved empirically by ingeniously employing a logistic regression differentiable layer within the calculation of coverage quality in our training loss. We show that the proposed training algorithms produce decisions that outperform the traditional estimate then optimize approaches.