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Data-Driven Two-Stage Conic Optimization with Zero-One Uncertainties

Anirudh Subramanyam (asubramanyam***at***anl.gov)
Mohamed El Tonbari (mtonbari***at***gatech.edu)
Kibaek Kim (kimk***at***anl.gov)

Abstract: We address high-dimensional zero-one random parameters in two-stage convex conic optimization problems. Such parameters typically represent failures of network elements and constitute rare, high-impact random events in several applications. Given a sparse training dataset of the parameters, we motivate and study a distributionally robust formulation of the problem using a Wasserstein ambiguity set centered at the empirical distribution. We present a simple, tractable, and conservative approximation of this problem that can be efficiently computed and iteratively improved. Our method relies on a reformulation that optimizes over the convex hull of a mixed-integer conic programming representable set, followed by an approximation of this convex hull using lift-and-project techniques. We illustrate the practical viability and strong out-of-sample performance of our method on nonlinear optimal power flow and multi-commodity network design problems that are affected by random contingencies, and we report improvements of up to 20\% over existing sample average approximation and two-stage robust optimization methods.

Keywords: Distributionally robust optimization, conic optimization, rare events, two-stage problems

Category 1: Robust Optimization

Category 2: Stochastic Programming


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Entry Submitted: 01/01/2020
Entry Accepted: 01/01/2020
Entry Last Modified: 07/16/2021

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