Conformal Uncertainty Sets for Robust Optimization

Decision-making under uncertainty is hugely important for any decisions sensitive to perturbations in observed data. One method of incorporating uncertainty into making optimal decisions is through robust optimization, which minimizes the worst-case scenario over some uncertainty set. We explore Mahalanobis distance as a novel function for multi-target regression and the construction of joint prediction regions. We also connect conformal prediction regions to robust optimization, providing finite sample valid and conservative uncertainty sets, aptly named conformal uncertainty sets. We compare the coverage and efficiency of the conformal prediction regions generated with Mahalanobis distance to other conformal prediction regions. We also construct a small robust optimization example to compare conformal uncertainty sets to those constructed under the assumption of normality.