Distributionally robust optimization using Haar wavelet ambiguity sets

Dimitris Boskos, Jorge Cortés and Sonia Martínez
Proceedings of the 61st IEEE Int. Conf. on Decision and Control, Cancun, Mexico, December 2022

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.

File: main.pdf

Bib-tex entry:

@InProceedings{DB-JC-SM:22-cdc,
author = {D. Boskos and J. Cort\'es and S. Mart{\'\i}nez},
title = {Distributionally robust optimization using Haar wavelet ambiguity sets},
booktitle = {61st IEEE Int. Conf. on Decision and Control},
pages = {},
year = {2022},
address = {Cancun, Mexico},
month = {December}
}