mlsanityData to 14 Oct 2026

Decision Making under Model Misspecification: DRO with Robust Bayesian Ambiguity Sets

arXiv 2505.03585 ↗First posted 6 May 2025stat.ML cs.LGcited by 2

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Abstract (arXiv)

Distributionally Robust Optimisation (DRO) protects risk-averse decision-makers by considering the worst-case risk within an ambiguity set of distributions based on the empirical distribution or a model. To further guard against finite, noisy data, model-based approaches admit Bayesian formulations that propagate uncertainty from the posterior to the decision-making problem. However, when the model is misspecified, the decision maker must stretch the ambiguity set to contain the data-generating process (DGP), leading to overly conservative decisions. We address this challenge by introducing DRO with Robust, to model misspecification, Bayesian Ambiguity Sets (DRO-RoBAS). These are Maximum Mean Discrepancy ambiguity sets centred at a robust posterior predictive distribution that incorporates beliefs about the DGP. We show that the resulting optimisation problem obtains a dual formulation in the Reproducing Kernel Hilbert Space and we give probabilistic guarantees on the tolerance level of the ambiguity set. Our method outperforms other Bayesian and empirical DRO approaches in out-of-sample performance on the Newsvendor and Portfolio problems with various cases of model misspecification.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 27 of its 49 references that are in the map. First posted on arXiv 6 May 2025.

Builds on

27 of 49 references.

References · 27

  1. 2021Towards Out-Of-Distribution Generalization: A Surveycited by 436
  2. 2015Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulationscited by 291
  3. 2016Distributionally Robust Stochastic Optimization with Wasserstein Distancecited by 185
  4. 2013A General Framework for Updating Belief Distributionscited by 175
  5. 2019Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learningcited by 170
  6. 2019Distributionally Robust Optimization and Generalization in Kernel Methodscited by 73
  7. 2020Coping with Label Shift via Distributionally Robust Optimisationcited by 70
  8. 2021Robust Generalised Bayesian Inference for Intractable Likelihoodscited by 53
  9. 2020Finite-Sample Guarantees for Wasserstein Distributionally Robust Optimization: Breaking the Curse of Dimensionalitycited by 49
  10. 2019Statistical Inference for Generative Models with Maximum Mean Discrepancycited by 45
  11. 2022Robust Bayesian Inference for Simulator-based Models via the MMD Posterior Bootstrapcited by 41
  12. 2019MMD-Bayes: Robust Bayesian Estimation via Maximum Mean Discrepancycited by 35
15 more
  1. 2021Modeling the Second Player in Distributionally Robust Optimizationcited by 29
  2. 2019Finite sample properties of parametric MMD estimation: robustness to misspecification and dependencecited by 25
  3. 2018Nonparametric learning from Bayesian models with randomized objective functionscited by 17
  4. 2022Distributionally Robust Models with Parametric Likelihood Ratioscited by 17
  5. 2019Scalable Nonparametric Sampling from Multimodal Posteriors with the Posterior Bootstrapcited by 16
  6. 2021Bayesian Distributionally Robust Optimizationcited by 16
  7. 2022Distributionally Robust Bayesian Optimization with varphi-divergencescited by 16
  8. 2023Robust and Scalable Bayesian Online Changepoint Detectioncited by 16
  9. 2023Outlier-Robust Wasserstein DROcited by 16
  10. 2023Robust and Conjugate Gaussian Process Regressioncited by 14
  11. 2025Robust and Conjugate Spatio-Temporal Gaussian Processescited by 9
  12. 2023Distributionally Robust Optimal and Safe Control of Stochastic Systems via Kernel Conditional Mean Embeddingcited by 6
  13. 2023Learning Against Distributional Uncertainty: On the Trade-off Between Robustness and Specificitycited by 4
  14. 2024Decision Making under the Exponential Family: Distributionally Robust Optimisation with Bayesian Ambiguity Setscited by 3
  15. 2022Distributionally Robust Decision Making Leveraging Conditional Distributionscited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026Bulk-Calibrated Credal Ambiguity Sets: Fast, Tractable Decision Making under Out-of-Sample Contaminationcited by 1
  2. 2026A Gradient Flow Perspective on Minimum MMD Estimationcited by 1