Deciphering Latent Uncertainty Sources with Principal Component Analysis for Adaptive Robust Optimization

Abstract This paper proposes a novel data-driven robust optimization framework that leverages the power of machine learning for decision-making under uncertainty. By performing principal component analysis on uncertainty data, the correlations among uncertain parameters are effectively captured, and latent uncertainty sources are identified. Uncertainty data are then projected onto each principal component to facilitate extracting distributional information of latent uncertainties with kernel density estimation technique. To explicitly account for asymmetric uncertainties, we introduce forward and backward deviation vectors in an uncertainty set. The resulting data-driven uncertainty set is general enough to be employed in adaptive robust optimization model. The proposed framework not only significantly ameliorates the conservatism of robust optimization but also enjoys computational efficiency and wide applicability. An application of optimization under uncertainty on batch process scheduling is presented to demonstrate the effectiveness of the proposed general framework. We also investigate a data-driven uncertainty set in a low-dimensional subspace and derive a theoretical bound on the performance gap between ARO solutions due to the dimension reduction of uncertainties.