Conformal Uncertainty Sets for Robust Optimization
This work addresses uncertainty in robust optimization for decision-making applications, representing an incremental advancement by integrating conformal prediction with existing methods.
The authors tackled the problem of decision-making under uncertainty by connecting conformal prediction regions to robust optimization, resulting in finite sample valid and conservative ellipsoidal uncertainty sets called conformal uncertainty sets.
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 connect conformal prediction regions to robust optimization, providing finite sample valid and conservative ellipsoidal uncertainty sets, aptly named conformal uncertainty sets. In pursuit of this connection we explicitly define Mahalanobis distance as a potential conformity score in full conformal prediction. We also compare the coverage and optimization performance of conformal uncertainty sets, specifically generated with Mahalanobis distance, to traditional ellipsoidal uncertainty sets on a collection of simulated robust optimization examples.