Distributionally Robust Optimization

arXiv:2411.02549 · math.OC, cs.LG, stat.ML · Submitted 2024-11-04 · Read on arXiv

math.OC, cs.LG, stat.ML

Submitted: 2024-11-04

Updated: 2025-05-26

Journal ref: Acta Numerica 34 (2025), 579-804

DOI: 10.1017/S0962492924000084

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Optimal Transport — 110× in this paper · explained in 5 episodes
• Loss Function — 90× in this paper · explained in 2 episodes
• Regularization — 67× in this paper · explained in 3 episodes
• Objective Function — 66× in this paper · explained in 2 episodes
• Wasserstein Distance — 59× in this paper · explained in 4 episodes
• Robustness — 30× in this paper · explained in 5 episodes
• Generalization — 22× in this paper · explained in 13 episodes
• Regret — 16× in this paper · explained in 3 episodes
• Consistency — 12× in this paper · explained in 3 episodes
• Adversarial Training — 10× in this paper · explained in 1 episode
• 2-Wasserstein Distance — 8× in this paper · explained in 1 episode
• Generalization Bounds — 8× in this paper · explained in 2 episodes
• Adversarial Examples — 6× in this paper · explained in 2 episodes
• Adversarial Attacks — 4× in this paper · explained in 1 episode
• Curse of Dimensionality — 4× in this paper · explained in 6 episodes
• Calibration — 3× in this paper · explained in 7 episodes
• Copula — 3× in this paper · explained in 2 episodes
• Nash Equilibrium — 3× in this paper · explained in 2 episodes
• Adaptation — 2× in this paper · explained in 1 episode
• Axioms — 2× in this paper · explained in 2 episodes
• Combinatorial Optimization — 2× in this paper · explained in 2 episodes
• Computational overhead — 2× in this paper · explained in 2 episodes
• Hilbert Space — 2× in this paper · explained in 2 episodes
• Minimax Regret — 2× in this paper · explained in 2 episodes
• Trace — 2× in this paper · explained in 2 episodes
• APEX — 1× in this paper · explained in 1 episode
• Adversarial Data Augmentation — 1× in this paper · explained in 1 episode
• Adversarial Robustness — 1× in this paper · explained in 3 episodes
• Aggregation — 1× in this paper · explained in 1 episode
• Alternating Direction Method of Multipliers (ADMM) — 1× in this paper · explained in 2 episodes
• Bayesian Optimization — 1× in this paper · explained in 3 episodes
• Clustering — 1× in this paper · explained in 2 episodes
• Computational Tractability — 1× in this paper · explained in 2 episodes
• Core — 1× in this paper · explained in 2 episodes
• Data Assimilation — 1× in this paper · explained in 2 episodes
• Data Augmentation — 1× in this paper · explained in 7 episodes
• Distribution Shift — 1× in this paper · explained in 6 episodes
• Domain Adaptation — 1× in this paper · explained in 5 episodes
• Feature Selection — 1× in this paper · explained in 4 episodes
• Gradient Flow — 1× in this paper · explained in 2 episodes
• Parsimony — 1× in this paper · explained in 2 episodes
• Phase Transitions — 1× in this paper · explained in 2 episodes
• Quantifying Uncertainty — 1× in this paper · explained in 5 episodes
• Quantization — 1× in this paper · explained in 12 episodes
• Semi-supervised Learning — 1× in this paper · explained in 4 episodes
• Sparsity — 1× in this paper · explained in 4 episodes
• Structural Constraints — 1× in this paper · explained in 2 episodes
• Transferability — 1× in this paper · explained in 4 episodes
• VC Dimension — 1× in this paper · explained in 2 episodes

Sources

• Distributional Uncertainty Propagation via Optimal Transport
• Wasserstein Distributionally Robust Estimation in High Dimensions: Performance Analysis and Optimal Hyperparameter Tuning
• A Distributionally Robust Optimization Framework for Extreme Event Estimation
• It's All in the Mix: Wasserstein Classification and Regression with Mixed Features
• Learning and Decision-Making with Data: Optimal Formulations and Phase Transitions
• Holistic Robust Data-Driven Decisions
• Unifying Distributionally Robust Optimization via Optimal Transport Theory
• Distributionally Robust Optimization and Robust Statistics
• From Distributional Robustness to Robust Statistics: A Confidence Sets Perspective
• Optimal Confidence Intervals via Moderate Deviations Theory
• Data-driven Multistage Distributionally Robust Linear Optimization with Nested Distance
• Wasserstein Distributionally Robust Optimization and Variation Regularization
• Higher-Order Expansion and Bartlett Correctability of Distributionally Robust Optimization
• Multi-level Monte-Carlo Gradient Methods for Stochastic Optimization with Biased Oracles
• Sensitivity of causal distributionally robust optimization
• The Distributionally Robust Infinite-Horizon LQR
• Distributionally Robust Kalman Filtering over Finite and Infinite Horizon
• On the Impossibility of Statistically Improving Empirical Optimization: A Second-Order Stochastic Dominance Perspective
• Shape-Constrained Distributional Optimization via Importance-Weighted Sample Average Approximation
• Orthounimodal Distributionally Robust Optimization: Representation, Computation and Multivariate Extreme Event Applications

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