# Ambiguity set and learning via Bregman and Wasserstein

arXiv: https://arxiv.org/abs/1705.08056 · HTML: https://mlsanity.com/paper/1705.08056/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2017.

## Built on by (most cited first, 4 of 4)

- [Mirror and Preconditioned Gradient Descent in Wasserstein Space](https://mlsanity.com/paper/2406.08938/) (2024)
- [Regularized Inverse Reinforcement Learning](https://mlsanity.com/paper/2010.03691/) (2020)
- [Transport information Bregman divergences](https://mlsanity.com/paper/2101.01162/) (2021)
- [Designing Ambiguity Sets for Distributionally Robust Optimization Using Structural Causal Optimal Transport](https://mlsanity.com/paper/2510.00599/) (2025)

## Abstract (arXiv)

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.