mlsanityData to 14 Oct 2026

Smoothed f-Divergence Distributionally Robust Optimization

arXiv 2306.14041 ↗First posted 24 Jun 2023math.OC cs.LG stat.MLcited by 7

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Abstract (arXiv)

In data-driven optimization, sample average approximation (SAA) is known to suffer from the so-called optimizer's curse that causes an over-optimistic evaluation of the solution performance. We argue that a special type of distributionallly robust optimization (DRO) formulation offers theoretical advantages in correcting for this optimizer's curse compared to simple ``margin'' adjustments to SAA and other DRO approaches: It attains a statistical bound on the out-of-sample performance, for a wide class of objective functions and distributions, that is nearly tightest in terms of exponential decay rate. This DRO uses an ambiguity set based on a Kullback Leibler (KL) divergence smoothed by the Wasserstein or L'evy-Prokhorov (LP) distance via a suitable distance optimization. Computationally, we also show that such a DRO, and its generalized versions using smoothed f-divergence, are not harder than DRO problems based on f-divergence or Wasserstein distances, rendering our DRO formulations both statistically optimal and computationally viable.

Key facts. Cited by 7 papers in the map (data through 14 Oct 2026). Builds on 26 of its 91 references that are in the map. First posted on arXiv 24 Jun 2023.

Builds on

26 of 91 references.

References · 26

  1. 2015Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulationscited by 291
  2. 2016Distributionally Robust Stochastic Optimization with Wasserstein Distancecited by 185
  3. 2016Statistics of Robust Optimization: A Generalized Empirical Likelihood Approachcited by 183
  4. 2019Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learningcited by 170
  5. 2016Variance-based regularization with convex objectivescited by 155
  6. 2017Regularization via Mass Transportationcited by 81
  7. 2019Distributionally Robust Optimization and Generalization in Kernel Methodscited by 73
  8. 2020Finite-Sample Guarantees for Wasserstein Distributionally Robust Optimization: Breaking the Curse of Dimensionalitycited by 49
  9. 2017From Data to Decisions: Distributionally Robust Optimization is Optimalcited by 38
  10. 2016Recovering Best Statistical Guarantees via the Empirical Divergence-based Distributionally Robust Optimizationcited by 33
  11. 2020Acceleration with a Ball Optimization Oraclecited by 31
  12. 2014Robust Sample Average Approximationcited by 25
14 more
  1. 2019Confidence Regions in Wasserstein Distributionally Robust Estimationcited by 24
  2. 2022Holistic Robust Data-Driven Decisionscited by 18
  3. 2020Distributional Robustness with IPMs and links to Regularization and GANscited by 17
  4. 2020Towards Optimal Problem Dependent Generalization Error Bounds in Statistical Learning Theorycited by 13
  5. 2016The Empirical Likelihood Approach to Quantifying Uncertainty in Sample Average Approximationcited by 12
  6. 2019Formulation and properties of a divergence used to compare probability measures without absolute continuitycited by 11
  7. 2021Generalization Bounds with Minimal Dependency on Hypothesis Class via Distributionally Robust Optimizationcited by 9
  8. 2021Learning and Decision-Making with Data: Optimal Formulations and Phase Transitionscited by 7
  9. 2016Sensitivity to Serial Dependency of Input Processes: A Robust Approachcited by 6
  10. 2017The discrete moment problem with nonconvex shape constraintscited by 6
  11. 2017Worst-Case Expected Shortfall with Univariate and Bivariate Marginalscited by 3
  12. 2019Tractable Reformulations of Distributionally Robust Two-stage Stochastic Programs with ∞-Wasserstein Distancecited by 3
  13. 2021Orthounimodal Distributionally Robust Optimization: Representation, Computation and Multivariate Extreme Event Applicationscited by 3
  14. 2023A Distributionally Robust Optimization Framework for Extreme Event Estimationcited by 2

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 2; 2024: 1; 2025: 2; 2026: 2.

7 papers.

  1. 2023Unifying Distributionally Robust Optimization via Optimal Transport Theorycited by 13
  2. 2025Nested Stochastic Algorithm for Generalized Sinkhorn distance-Regularized Distributionally Robust Optimizationcited by 3
  3. 2023Optimal Transport Regularized Divergences: Application to Adversarial Robustnesscited by 2
  4. 2024From Distributional Robustness to Robust Statistics: A Confidence Sets Perspectivecited by 1
  5. 2025A Dual Optimization View to Empirical Risk Minimization with f-Divergence Regularizationcited by 1
  6. 2026Statistical Guarantees for Distributionally Robust Optimization with Optimal Transport and OT-Regularized Divergencescited by 0
  7. 2026Adversarial Training for Deep Hedging in Nonstationary Marketscited by 0