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

arXiv: https://arxiv.org/abs/2510.11169 · HTML: https://mlsanity.com/paper/2510.11169/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 61 references that are in the map.
- First posted on arXiv 13 Oct 2025.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data](https://mlsanity.com/paper/1703.11008/) (2017)
- [OpenML: networked science in machine learning](https://mlsanity.com/paper/1407.7722/) (2014)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Tighter risk certificates for neural networks](https://mlsanity.com/paper/2007.12911/) (2020)
- [Entropy-SGD optimizes the prior of a PAC-Bayes bound: Generalization properties of Entropy-SGD and data-dependent priors](https://mlsanity.com/paper/1712.09376/) (2017)
- [PAC-Bayes Analysis Beyond the Usual Bounds](https://mlsanity.com/paper/2006.13057/) (2020)
- [Adaptive Sampling for Stochastic Risk-Averse Learning](https://mlsanity.com/paper/1910.12511/) (2019)
- [Learning Bounds for Risk-sensitive Learning](https://mlsanity.com/paper/2006.08138/) (2020)
- [A General Framework for the Practical Disintegration of PAC-Bayesian Bounds](https://mlsanity.com/paper/2102.08649/) (2021)
- [PAC-Bayesian Bound for the Conditional Value at Risk](https://mlsanity.com/paper/2006.14763/) (2020)
- [Leveraging PAC-Bayes Theory and Gibbs Distributions for Generalization Bounds with Complexity Measures](https://mlsanity.com/paper/2402.13285/) (2024)

## Built on by (most cited first, 1 of 1)

- [On the disintegration of the stochastic majority vote: From PAC-Bayesian bounds to a self-bounding algorithm](https://mlsanity.com/paper/2609.16803/) (2026)

## Abstract (arXiv)

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 overcome 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 disintegratedPAC-Bayesian guarantees beyond standard risks. Building on this theory, we design a self-bounding algorithm that minimizes our bounds directly, yielding models with guarantees at the subgroup level. Finally, we empirically demonstrate the usefulness of our approach.