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Statistics of Robust Optimization: A Generalized Empirical Likelihood Approach

arXiv 1610.03425 ↗First posted 11 Oct 2016stat.MLcited by 182

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Abstract (arXiv)

We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotically. We develop a generalized empirical likelihood framework---based on distributional uncertainty sets constructed from nonparametric f-divergence balls---for Hadamard differentiable functionals, and in particular, stochastic optimization problems. As consequences of this theory, we provide a principled method for choosing the size of distributional uncertainty regions to provide one- and two-sided confidence intervals that achieve exact coverage. We also give an asymptotic expansion for our distributionally robust formulation, showing how robustification regularizes problems by their variance. Finally, we show that optimizers of the distributionally robust formulations we study enjoy (essentially) the same consistency properties as those in classical sample average approximations. Our general approach applies to quickly mixing stationary sequences, including geometrically ergodic Harris recurrent Markov chains.

Key facts. Cited by 182 papers in the map (data through 7 Oct 2026). First posted on arXiv 11 Oct 2016.

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Citing papers per year: 2021: 36; 2022: 41; 2023: 38; 2024: 31; 2025: 19; 2026: 17.

182 papers.

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  1. 2021Just Train Twice: Improving Group Robustness without Training Group Informationcited by 522
  2. 2021Towards Out-Of-Distribution Generalization: A Surveycited by 431
  3. 2021Measure and Improve Robustness in NLP Models: A Surveycited by 107
  4. 2022MaskTune: Mitigating Spurious Correlations by Forcing to Explorecited by 66
  5. 2022MEDFAIR: Benchmarking Fairness for Medical Imagingcited by 66
  6. 2021Examining and Combating Spurious Features under Distribution Shiftcited by 64
  7. 2021Mandoline: Model Evaluation under Distribution Shiftcited by 55
  8. 2022AutoBalance: Optimized Loss Functions for Imbalanced Datacited by 49
  9. 2021Unsupervised Learning of Debiased Representations with Pseudo-Attributescited by 44
  10. 2023Model Agnostic Sample Reweighting for Out-of-Distribution Learningcited by 43
  11. 2021Out-of-distribution Generalization in the Presence of Nuisance-Induced Spurious Correlationscited by 41
  12. 2021Sinkhorn Distributionally Robust Optimizationcited by 38
38 more
  1. 2021Deeply-Debiased Off-Policy Interval Estimationcited by 36
  2. 2022A Unified Wasserstein Distributional Robustness Framework for Adversarial Trainingcited by 36
  3. 2023A Finite Sample Complexity Bound for Distributionally Robust Q-learningcited by 35
  4. 2021Regularized Policies are Reward Robustcited by 32
  5. 2022Minimax Regret Optimization for Robust Machine Learning under Distribution Shiftcited by 31
  6. 2022Distributionally Robust Offline Reinforcement Learning with Linear Function Approximationcited by 31
  7. 2024Applied Causal Inference Powered by ML and AIcited by 30
  8. 2021Modeling the Second Player in Distributionally Robust Optimizationcited by 29
  9. 2021On the Optimality of Batch Policy Optimization Algorithmscited by 28
  10. 2021Towards Theoretical Understandings of Robust Markov Decision Processes: Sample Complexity and Asymptoticscited by 27
  11. 2021Statistical Analysis of Wasserstein Distributionally Robust Estimatorscited by 27
  12. 2021Simple and near-optimal algorithms for hidden stratification and multi-group learningcited by 26
  13. 2023Not All Semantics are Created Equal: Contrastive Self-supervised Learning with Automatic Temperature Individualizationcited by 25
  14. 2021Measuring Generalization with Optimal Transportcited by 24
  15. 2022MetaSets: Meta-Learning on Point Sets for Generalizable Representationscited by 22
  16. 2023Augmented balancing weights as linear regressioncited by 21
  17. 2024Adaptive Preference Scaling for Reinforcement Learning with Human Feedbackcited by 20
  18. 2021Distributionally Robust Multilingual Machine Translationcited by 18
  19. 2021Learning Representations that Support Robust Transfer of Predictorscited by 17
  20. 2022Holistic Robust Data-Driven Decisionscited by 17
  21. 2025Vulnerability-Aware Alignment: Mitigating Uneven Forgetting in Harmful Fine-Tuningcited by 17
  22. 2022Distributionally Robust Bayesian Optimization with varphi-divergencescited by 16
  23. 2022Stochastic Constrained DRO with a Complexity Independent of Sample Sizecited by 16
  24. 2023Distributionally Robust Post-hoc Classifiers under Prior Shiftscited by 16
  25. 2021Are Bias Mitigation Techniques for Deep Learning Effective?cited by 14
  26. 2021Toward Learning Human-aligned Cross-domain Robust Models by Countering Misaligned Featurescited by 14
  27. 2023Towards Artificial General Intelligence (AGI) in the Internet of Things (IoT): Opportunities and Challengescited by 14
  28. 2021Statistical inference for individual fairnesscited by 13
  29. 2023Distributionally Robust Recourse Actioncited by 12
  30. 2021Label Distributionally Robust Losses for Multi-class Classification: Consistency, Robustness and Adaptivitycited by 11
  31. 2022Global-Local Regularization Via Distributional Robustnesscited by 11
  32. 2022Understanding new tasks through the lens of training data via exponential tiltingcited by 11
  33. 2022Certifying Some Distributional Fairness with Subpopulation Decompositioncited by 11
  34. 2024Efficient Algorithms for Empirical Group Distributionally Robust Optimization and Beyondcited by 11
  35. 2021Coordinate Linear Variance Reduction for Generalized Linear Programmingcited by 10
  36. 2022What You See is What You Get: Principled Deep Learning via Distributional Generalizationcited by 10
  37. 2022AGRO: Adversarial Discovery of Error-prone groups for Robust Optimizationcited by 10
  38. 2023ArCL: Enhancing Contrastive Learning with Augmentation-Robust Representationscited by 10

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