End-to-end Conditional Robust Optimization
This work addresses safety and reliability in high-stakes applications like contextual optimization, but it is incremental as it builds on existing CRO and differentiable optimization methods.
The paper tackles the problem of training Conditional Robust Optimization (CRO) models for safe decision-making under uncertainty by proposing an end-to-end approach that optimizes both empirical risk and conditional coverage quality, showing it outperforms traditional methods.
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.