Distributionally Robust Optimization via Haar Wavelet Ambiguity Sets

Conference paper (2022)

Authors

D. Boskos Team Dimitris Boskos - Mechanical, Maritime and Materials Engineering
Jorge Cortes University of California
S. Martinez Sandez Design for Sustainability - IDE , University of California
Research Group
Team Dimitris Boskos (Mechanical, Maritime and Materials Engineering) (TU Delft)
Copyright: © 2022 D. Boskos, Jorge Cortes, S. Martinez Sandez
DOI: https://doi.org/10.1109/CDC51059.2022.9993084
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Published Date

2022

Language

English

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Faculty

Mechanical, Maritime and Materials Engineering

Department

Delft Center for Systems and Control

Research Group

Team Dimitris Boskos

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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