End-to-end Conditional Robust Optimization
Abhilash Chenreddy Erick Delage
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.