Jianqiang Cheng – Optimization Online

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

Published: 2026/05/28, Updated: 2026/07/05

Optimization in Data Science, Robust Optimization, Stochastic Programming distributionally robust optimization, heavy-tailed distributions, incomplete data, integral probability metrics, markovian data, outlier-corrupted data, semi-infinite programming

Distributionally robust optimization (DRO) provides a principled framework for decision-making under distributional uncertainty. Classical data-driven DRO frameworks typically construct ambiguity sets from distributional information, such as moment constraints, divergence neighborhoods, or Wasserstein balls, specified before the downstream loss is considered. We propose a task-aware DRO framework based on targeted integral probability metrics. The ambiguity set … Read more

Distributionally Robust Optimization with Principal Component Analysis

Published: 2016/05/18, Updated: 2018/04/27

Robust Optimization, Stochastic Programming distributionally robust optimization, principal component analysis, semidefinite programming, stochastic programming

Distributionally robust optimization (DRO) is widely used, because it offers a way to overcome the conservativeness of robust optimization without requiring the specificity of stochastic optimization. On the computational side, many practical DRO instances can be equivalently (or approximately) formulated as semidefinite programming (SDP) problems via conic duality of the moment problem. However, despite being … Read more