Jorge Cortés
Professor
Cymer Corporation Endowed Chair
Distributionally robust optimization via Haar wavelet ambiguity sets
D. Boskos, J. Cortés, S. Martínez
Proceedings of the IEEE Conference on Decision and Control, Cancun, Mexico, 2022, pp. 4782-4787
Abstract
This paper introduces a spectral parameterization of ambiguity sets to
hedge against distributional uncertainty in stochastic optimization
problems. We build an ambiguity set of probability densities around a
histogram estimator, which is constructed by independent samples from
the unknown distribution. The densities in the ambiguity set are
determined by bounding the distance between the coefficients of their
Haar wavelet expansion and the expansion of the histogram
estimator. This representation facilitates the computation of
expectations, leading to tractable minimax problems that are linear in
the parameters of the ambiguity set, and enables the inclusion of
additional constraints that can capture valuable prior information
about the unknown distribution.
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Mechanical and Aerospace Engineering,
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