Decomposition Algorithm for Distributionally Robust Optimization using Wasserstein Metric

2017/04/12 by Fengqiao Luo, Sanjay Mehrotra, Luo, Fengqiao +1 · 5 citations
Decision Sciences · Mathematics · #FOS: Mathematics #Fuzzy Systems and Optimization #Optimization and Control (math.OC) #Probabilistic and Robust Engineering Design #Risk and Portfolio Optimization

paper · pdf · doi:10.48550/arxiv.1704.03920

openalex publication_date 2017/04/12 · openalex created_date 2017/04/28 · openalex updated_date 2026/07/28

Abstract

We study distributionally robust optimization (DRO) problems where the ambiguity set is defined using the Wasserstein metric. We show that this class of DRO problems can be reformulated as semi-infinite programs. We give an exchange method to solve the reformulated problem for the general nonlinear model, and a central cutting-surface method for the convex case, assuming that we have a separation oracle. We used a distributionally robust generalization of the logistic regression model to test our algorithm. Numerical experiments on the distributionally robust logistic regression models show that the number of oracle calls are typically 20 ? 50 to achieve 5-digit precision. The solution found by the model is generally better in its ability to predict with a smaller standard error.

Citations

• Semidefinite programming relaxations for semialgebraic problems
• On Distributionally Robust Chance-Constrained Linear Programs
• Robust optimization ? methodology and applications
• Distributionally robust joint chance constraints with second-order moment information
• Receiver-operating characteristic (ROC) plots: a fundamental evaluation tool in clinical medicine
• On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming
• Data-Driven Robust Optimization
• On the rate of convergence in Wasserstein distance of the empirical\n measure
• Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations

Cited by

• Explicit Reformulation of Discrete Distributionally Robust Optimization Problems
• Multi-Agent Inverse Reinforcement Learning for Identifying Pareto-Efficient Coordination -- A Distributionally Robust Approach
• Tractable Reformulations of Distributionally Robust Two-stage Stochastic Programs with ∞-Wasserstein Distance
• Unbiased Gradient Estimation for Distributionally Robust Learning
• Wasserstein Distributionally Robust Inverse Multiobjective Optimization

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