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Ambiguity set and learning via Bregman and Wasserstein

2017/05/23 by Xin Guo, Guo, Xin, Johnny Hong +3 · 2 citations
Decision Sciences · Mathematics · #Advanced Statistical Methods and Models #FOS: Computer and information sciences #Fuzzy Systems and Optimization #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Risk and Portfolio Optimization

paper · pdf · doi:10.48550/arxiv.1705.08056

openalex publication_date 2017/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Construction of ambiguity set in robust optimization relies on the choice of divergences between probability distributions. In distribution learning, choosing appropriate probability distributions based on observed data is critical for approximating the true distribution. To improve the performance of machine learning models, there has recently been interest in designing objective functions based on Lp-Wasserstein distance rather than the classical Kullback-Leibler (KL) divergence. In this paper, we derive concentration and asymptotic results using Bregman divergence. We propose a novel asymmetric statistical divergence called Wasserstein-Bregman divergence as a generalization of L2-Wasserstein distance. We discuss how these results can be applied to the construction of ambiguity set in robust optimization.

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