Decision Making under the Exponential Family: Distributionally Robust Optimisation with Bayesian Ambiguity Sets

Charita Dellaporta, Patrick O’Hara, Theodoros Damoulas
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:13011-13043, 2025.

Abstract

Decision making under uncertainty is challenging as the data-generating process (DGP) is often unknown. Bayesian inference proceeds by estimating the DGP through posterior beliefs on the model’s parameters. However, minimising the expected risk under these beliefs can lead to suboptimal decisions due to model uncertainty or limited, noisy observations. To address this, we introduce Distributionally Robust Optimisation with Bayesian Ambiguity Sets (DRO-BAS) which hedges against model uncertainty by optimising the worst-case risk over a posterior-informed ambiguity set. We provide two such sets, based on the posterior expectation (DRO-BAS(PE)) or the posterior predictive (DRO-BAS(PP)) and prove that both admit, under conditions, strong dual formulations leading to efficient single-stage stochastic programs which are solved with a sample average approximation. For DRO-BAS(PE), this covers all conjugate exponential family members while for DRO-BAS(PP) this is shown under conditions on the predictive’s moment generating function. Our DRO-BAS formulations outperform existing Bayesian DRO on the Newsvendor problem and achieve faster solve times with comparable robustness on the Portfolio problem.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-dellaporta25a, title = {Decision Making under the Exponential Family: Distributionally Robust Optimisation with {B}ayesian Ambiguity Sets}, author = {Dellaporta, Charita and O'Hara, Patrick and Damoulas, Theodoros}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {13011--13043}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/dellaporta25a/dellaporta25a.pdf}, url = {https://proceedings.mlr.press/v267/dellaporta25a.html}, abstract = {Decision making under uncertainty is challenging as the data-generating process (DGP) is often unknown. Bayesian inference proceeds by estimating the DGP through posterior beliefs on the model’s parameters. However, minimising the expected risk under these beliefs can lead to suboptimal decisions due to model uncertainty or limited, noisy observations. To address this, we introduce Distributionally Robust Optimisation with Bayesian Ambiguity Sets (DRO-BAS) which hedges against model uncertainty by optimising the worst-case risk over a posterior-informed ambiguity set. We provide two such sets, based on the posterior expectation (DRO-BAS(PE)) or the posterior predictive (DRO-BAS(PP)) and prove that both admit, under conditions, strong dual formulations leading to efficient single-stage stochastic programs which are solved with a sample average approximation. For DRO-BAS(PE), this covers all conjugate exponential family members while for DRO-BAS(PP) this is shown under conditions on the predictive’s moment generating function. Our DRO-BAS formulations outperform existing Bayesian DRO on the Newsvendor problem and achieve faster solve times with comparable robustness on the Portfolio problem.} }
Endnote
%0 Conference Paper %T Decision Making under the Exponential Family: Distributionally Robust Optimisation with Bayesian Ambiguity Sets %A Charita Dellaporta %A Patrick O’Hara %A Theodoros Damoulas %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-dellaporta25a %I PMLR %P 13011--13043 %U https://proceedings.mlr.press/v267/dellaporta25a.html %V 267 %X Decision making under uncertainty is challenging as the data-generating process (DGP) is often unknown. Bayesian inference proceeds by estimating the DGP through posterior beliefs on the model’s parameters. However, minimising the expected risk under these beliefs can lead to suboptimal decisions due to model uncertainty or limited, noisy observations. To address this, we introduce Distributionally Robust Optimisation with Bayesian Ambiguity Sets (DRO-BAS) which hedges against model uncertainty by optimising the worst-case risk over a posterior-informed ambiguity set. We provide two such sets, based on the posterior expectation (DRO-BAS(PE)) or the posterior predictive (DRO-BAS(PP)) and prove that both admit, under conditions, strong dual formulations leading to efficient single-stage stochastic programs which are solved with a sample average approximation. For DRO-BAS(PE), this covers all conjugate exponential family members while for DRO-BAS(PP) this is shown under conditions on the predictive’s moment generating function. Our DRO-BAS formulations outperform existing Bayesian DRO on the Newsvendor problem and achieve faster solve times with comparable robustness on the Portfolio problem.
APA
Dellaporta, C., O’Hara, P. & Damoulas, T.. (2025). Decision Making under the Exponential Family: Distributionally Robust Optimisation with Bayesian Ambiguity Sets. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:13011-13043 Available from https://proceedings.mlr.press/v267/dellaporta25a.html.

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