Conformal uncertainty sets for robust optimization

Chancellor Johnstone, Bruce Cox
Proceedings of the Tenth Symposium on Conformal and Probabilistic Prediction and Applications, PMLR 152:72-90, 2021.

Abstract

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 \emph{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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v152-johnstone21a, title = {Conformal uncertainty sets for robust optimization}, author = {Johnstone, Chancellor and Cox, Bruce}, booktitle = {Proceedings of the Tenth Symposium on Conformal and Probabilistic Prediction and Applications}, pages = {72--90}, year = {2021}, editor = {Carlsson, Lars and Luo, Zhiyuan and Cherubin, Giovanni and An Nguyen, Khuong}, volume = {152}, series = {Proceedings of Machine Learning Research}, month = {08--10 Sep}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v152/johnstone21a/johnstone21a.pdf}, url = {https://proceedings.mlr.press/v152/johnstone21a.html}, abstract = {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 \emph{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.} }
Endnote
%0 Conference Paper %T Conformal uncertainty sets for robust optimization %A Chancellor Johnstone %A Bruce Cox %B Proceedings of the Tenth Symposium on Conformal and Probabilistic Prediction and Applications %C Proceedings of Machine Learning Research %D 2021 %E Lars Carlsson %E Zhiyuan Luo %E Giovanni Cherubin %E Khuong An Nguyen %F pmlr-v152-johnstone21a %I PMLR %P 72--90 %U https://proceedings.mlr.press/v152/johnstone21a.html %V 152 %X 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 \emph{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.
APA
Johnstone, C. & Cox, B.. (2021). Conformal uncertainty sets for robust optimization. Proceedings of the Tenth Symposium on Conformal and Probabilistic Prediction and Applications, in Proceedings of Machine Learning Research 152:72-90 Available from https://proceedings.mlr.press/v152/johnstone21a.html.

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