PAC-Bayesian Bounds on Constrained $f$-Entropic Risk Measures

Hind Atbir, Farah Cherfaoui, Guillaume Metzler, Emilie Morvant, Paul Viallard
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:2017-2025, 2026.

Abstract

PAC generalization bounds on the risk, when expressed in terms of the expected loss, are often insufficient to capture imbalances between subgroups in the data. To tackle this limitation, we introduce a new family of risk measures, called constrained $f$-entropic risk measures, which enable finer control over distributional shifts and subgroup imbalances via $f$-divergences, and include the Conditional Value at Risk (CVaR), a well-known risk measure. We derive both classical and disintegrated PAC-Bayesian generalization bounds for this family of risks, providing the first disintegrated PAC-Bayesian guarantees beyond standard risks. Building on this theory, we design a self-bounding algorithm minimizing our bounds directly, yielding models with guarantees at the subgroup level. We empirically demonstrate the usefulness of our approach.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-atbir26a, title = { PAC-Bayesian Bounds on Constrained $f$-Entropic Risk Measures }, author = {Atbir, Hind and Cherfaoui, Farah and Metzler, Guillaume and Morvant, Emilie and Viallard, Paul}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {2017--2025}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/atbir26a/atbir26a.pdf}, url = {https://proceedings.mlr.press/v300/atbir26a.html}, abstract = { PAC generalization bounds on the risk, when expressed in terms of the expected loss, are often insufficient to capture imbalances between subgroups in the data. To tackle this limitation, we introduce a new family of risk measures, called constrained $f$-entropic risk measures, which enable finer control over distributional shifts and subgroup imbalances via $f$-divergences, and include the Conditional Value at Risk (CVaR), a well-known risk measure. We derive both classical and disintegrated PAC-Bayesian generalization bounds for this family of risks, providing the first disintegrated PAC-Bayesian guarantees beyond standard risks. Building on this theory, we design a self-bounding algorithm minimizing our bounds directly, yielding models with guarantees at the subgroup level. We empirically demonstrate the usefulness of our approach. } }
Endnote
%0 Conference Paper %T PAC-Bayesian Bounds on Constrained $f$-Entropic Risk Measures %A Hind Atbir %A Farah Cherfaoui %A Guillaume Metzler %A Emilie Morvant %A Paul Viallard %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-atbir26a %I PMLR %P 2017--2025 %U https://proceedings.mlr.press/v300/atbir26a.html %V 300 %X PAC generalization bounds on the risk, when expressed in terms of the expected loss, are often insufficient to capture imbalances between subgroups in the data. To tackle this limitation, we introduce a new family of risk measures, called constrained $f$-entropic risk measures, which enable finer control over distributional shifts and subgroup imbalances via $f$-divergences, and include the Conditional Value at Risk (CVaR), a well-known risk measure. We derive both classical and disintegrated PAC-Bayesian generalization bounds for this family of risks, providing the first disintegrated PAC-Bayesian guarantees beyond standard risks. Building on this theory, we design a self-bounding algorithm minimizing our bounds directly, yielding models with guarantees at the subgroup level. We empirically demonstrate the usefulness of our approach.
APA
Atbir, H., Cherfaoui, F., Metzler, G., Morvant, E. & Viallard, P.. (2026). PAC-Bayesian Bounds on Constrained $f$-Entropic Risk Measures . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:2017-2025 Available from https://proceedings.mlr.press/v300/atbir26a.html.

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