Data-Driven Methods for Robust Optimization Under Uncertainty

Anirudh Subramanyam, Argonne National Laboratory

The goal of data-driven optimization methods is to hedge against uncertainty in parameters whose distributions are observable only through a finite amount of training data and to learn decisions that can perform well on unseen testing data. This is challenging, however, if the dimension of the uncertainty is large or if the training dataset is sparse.

This talk will address high-dimensional discrete uncertainties in loss functions that solve a conic optimization problem. The latter have great modeling flexibility, and encompass several loss functions in classification and regression, and virtually all of (two-stage) convex optimization. Moreover, the discrete nature of the uncertainties arise naturally in network applications, where they can model rare, high-impact random failures of network elements.

Given a sparse training dataset, we motivate a formulation that seeks decisions that perform well under adverse distributions within a Wasserstein distance from the empirical distribution, and show some its conceptual benefits. We then present a simple and tractable approximation that can be efficiently computed at scale. The practical viability and strong out-of-sample performance of our method are illustrated via optimal power flow problems affected by rare network contingencies.

The first half of the talk will serve as a gentle introduction to data-driven robust formulations, whereas the second half of the talk will focus on high-dimensional discrete uncertainties in conic optimization.

This seminar will be streamed.

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