curse of dimensionality – Optimization Online

Distributionally Robust Optimization via Targeted Integral Probability Metrics for General Data Processes

Published: 2026/05/28

Optimization in Data Science, Robust Optimization, Stochastic Programming Contextual optimization, corrupted and missing data, curse of dimensionality, distributionally robust optimization, heavy-tailed distributions, integral probability metrics, markovian data

Distributionally robust optimization (DRO) has been successful in addressing decision-making problems under uncertainty when the underlying distribution is unknown. Existing data-driven DRO frameworks, however, often impose restrictive assumptions on the data-generating process. We propose a new DRO framework based on targeted integral probability metrics. The ambiguity set is defined directly through the loss functions induced … Read more

Projection Robust Wasserstein Barycenters

Published: 2021/09/28, Updated: 2021/09/29

Minhui Huang

Shiqian Ma

Lifeng Lai

Nonlinear Optimization curse of dimensionality, riemannian optimization, wasserstein barycenter

Collecting and aggregating information from several probability measures or histograms is a fundamental task in machine learning. One of the popular solution methods for this task is to compute the barycenter of the probability measures under the Wasserstein metric. However, approximating the Wasserstein barycenter is numerically challenging because of the curse of dimensionality. This paper … Read more