Keywords: Robust Optimization, Contextual Optimization, Conditional Stochastic Optimization, Unsupervised learning, Deep Neural Networks, Conditional Robust Optimization
TL;DR: Designing contextual uncertainty sets using Deep Neural Networks which are used in solving Conditional Robust Optimization problems.
Abstract: In this paper, we study a novel approach for data-driven decision-making under uncertainty in the presence of contextual information. Specifically, we solve this problem from a Conditional Robust Optimization (CRO) point of view. We propose an integrated framework that designs the conditional uncertainty set by jointly learning the partitions in the covariate data space and simultaneously constructing partition specific deep uncertainty sets for the random vector that perturbs the CRO problem. We also provide theoretical guarantees for the coverage of the uncertainty sets and value at risk performances obtained using the proposed CRO approach. Finally, we use the simulated and real world data to show the implementation of our approach and compare it against two non-contextual benchmark approaches to demonstrate the value of exploiting contextual information in robust optimization.
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