Sinkhorn Distributionally Robust Optimization

2021/09/24 by Jie Wang, Rui Gao, Wang, Jie +3 · 10 citations
Computer Science · Decision Sciences · #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Optimization and Control (math.OC) #Optimization and Variational Analysis #Probabilistic and Robust Engineering Design #Risk and Portfolio Optimization

paper · pdf · doi:10.48550/arxiv.2109.11926

openalex publication_date 2021/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study distributionally robust optimization with Sinkhorn distance -- a variant of Wasserstein distance based on entropic regularization. We derive a convex programming dual reformulation for general nominal distributions, transport costs, and loss functions. To solve the dual reformulation, we develop a stochastic mirror descent algorithm with biased subgradient estimators and derive its computational complexity guarantees. Finally, we provide numerical examples using synthetic and real data to demonstrate its superior performance.

Citations

• Distributionally Robust Stochastic Optimization with Wasserstein Distance
• Natural gradient via optimal transport
• Distributionally Robust Reinforcement Learning
• Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations
• Wasserstein Robust Reinforcement Learning
• A First-Order Algorithmic Framework for Wasserstein Distributionally Robust Logistic Regression
• On distributionally robust chance constrained programs with Wasserstein distance
• A Distributionally Robust Approach to Fair Classification
• Robustifying Conditional Portfolio Decisions via Optimal Transport

Cited by

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• Distributionally Robust Shape and Topology Optimization
• Duality and Policy Evaluation in Distributionally Robust Bayesian Diffusion Control
• Cross-Dock Door Design under Uncertainty: A two-stage DRO-based lower- and upper-bounding scheme
• DRO: A Python Library for Distributionally Robust Optimization in Machine Learning
• Distributionally Robust Deep Q-Learning

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• Iterative Sampling Methods for Sinkhorn Distributionally Robust Optimization
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• Sinkhorn Algorithm as a Special Case of Stochastic Mirror Descent