Loss-aware distributionally robust optimization via trainable optimal transport ambiguity sets

2025/09/16 by Jonas Ohnemus, Ohnemus, Jonas, Marta Fochesato +5
Business, Management and Accounting · Decision Sciences · #FOS: Electrical engineering #FOS: Mathematics #Forecasting Techniques and Applications #Optimization and Control (math.OC) #Risk and Portfolio Optimization #Supply Chain and Inventory Management #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2509.12689

openalex publication_date 2025/09/16 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28

Abstract

Optimal-Transport Distributionally Robust Optimization (OT-DRO) robustifies data-driven decision-making under uncertainty by capturing the sampling-induced statistical error via optimal transport ambiguity sets. The standard OT-DRO pipeline consists of a two-step procedure, where the ambiguity set is first designed and subsequently embedded into the downstream OT-DRO problem. However, this separation between uncertainty quantification and optimization might result in excessive conservatism. We introduce an end-to-end pipeline to automatically learn decision-focused ambiguity sets for OT-DRO problems, where the loss function informs the shape of the optimal transport ambiguity set, leading to less conservative yet distributionally robust decisions. We formulate the learning problem as a bilevel optimization program and solve it via a hypergradient-based method. By leveraging the recently introduced nonsmooth conservative implicit function theorem, we establish convergence to a critical point of the bilevel problem. We present experiments validating our method on standard portfolio optimization and linear regression tasks.

Citations

• Differentiable Distributionally Robust Optimization Layers
• Inexact subgradient methods for semialgebraic functions
• End-to-end Conditional Robust Optimization
• BP-MPC: Optimizing the Closed-Loop Performance of MPC using BackPropagation
• Structured ambiguity sets for distributionally robust optimization
• A Survey of Contextual Optimization Methods for Decision Making under Uncertainty
• Learning Decision-Focused Uncertainty Sets in Robust Optimization
• Distributionally Robust Linear Quadratic Control
• Predict-then-Calibrate: A New Perspective of Robust Contextual LP
• Wasserstein Tube MPC with Exact Uncertainty Propagation
• Distributionally Robust Optimization using Cost-Aware Ambiguity Sets
• Differentiating Nonsmooth Solutions to Parametric Monotone Inclusion Problems
• Distributionally Robust End-to-End Portfolio Construction
• Distributionally Robust Bootstrap Optimization
• Mean-Covariance Robust Risk Measurement
• Distributionally Robust Learning
• The Perils of Learning Before Optimizing
• Fast Distributionally Robust Learning with Variance Reduced Min-Max Optimization
• Interior Point Solving for LP-based prediction+optimisation
• Fast Epigraphical Projection-based Incremental Algorithms for Wasserstein Distributionally Robust Support Vector Machine
• Adversarial Classification via Distributional Robustness with Wasserstein Ambiguity
• On Linear Optimization over Wasserstein Balls
• Optimizing Percentile Criterion Using Robust MDPs
• Conservative set valued fields, automatic differentiation, stochastic gradient method and deep learning
• Wasserstein Distributionally Robust Optimization: Theory and\n Applications in Machine Learning
• Differentiating Through a Cone Program
• Solution Refinement at Regular Points of Conic Problems
• Melding the Data-Decisions Pipeline: Decision-Focused Learning for Combinatorial Optimization
• Stochastic subgradient method converges on tame functions
• Distributionally Robust Mean-Variance Portfolio Selection with Wasserstein Distances
• Regularization via Mass Transportation
• Smart "Predict, then Optimize"
• OptNet: Differentiable Optimization as a Layer in Neural Networks
• Distributionally Robust Stochastic Optimization with Wasserstein Distance
• Distributionally Robust Stochastic Optimization with Wasserstein Distance
• Quantifying Distributional Model Risk via Optimal Transport
• Distributionally Robust Logistic Regression
• Data-driven Distributionally Robust Optimization Using the Wasserstein\n Metric: Performance Guarantees and Tractable Reformulations
• Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations
• A Survey on Metric Learning for Feature Vectors and Structured Data
• Envelope Theorems for Arbitrary Choice Sets

Related

• Structured ambiguity sets for distributionally robust optimization
• Distributionally Robust Optimization
• Distributionally Robust Performative Optimization
• Distributionally Robust Optimization using Cost-Aware Ambiguity Sets
• Tractable reformulations of DRO problems over structured optimal transport ambiguity sets