mlsanityData to 7 Oct 2026

A Dual Optimization View to Empirical Risk Minimization with f-Divergence Regularization

arXiv 2508.03314 ↗First posted 5 Aug 2025stat.ML cs.LGcited by 1

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Abstract (arXiv)

The dual formulation of empirical risk minimization with f-divergence regularization (ERM-fDR) is introduced. The solution of the dual optimization problem to the ERM-fDR is connected to the notion of normalization function introduced as an implicit function. This dual approach leverages the Legendre-Fenchel transform and the implicit function theorem to provide a nonlinear ODE expression to the normalization function. Furthermore, the nonlinear ODE expression and its properties provide a computationally efficient method to calculate the normalization function of the ERM-fDR solution under a mild condition.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 16 of its 47 references that are in the map. First posted on arXiv 5 Aug 2025.

Builds on

16 of 47 references.

References · 16

  1. 2019Tightening Mutual Information Based Bounds on Generalization Errorcited by 117
  2. 2017User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradientcited by 116
  3. 2015How much does your data exploration overfit? Controlling bias via information usagecited by 95
  4. 2019Generalization Error Bounds Via R'enyi-, f-Divergences and Maximal Leakagecited by 48
  5. 2020When Optimizing f-divergence is Robust with Label Noisecited by 44
  6. 2020Non-exponentially weighted aggregation: regret bounds for unbounded loss functionscited by 18
  7. 2022Empirical Risk Minimization with Relative Entropy Regularizationcited by 13
  8. 2023On the Validation of Gibbs Algorithms: Training Datasets, Test Datasets and their Aggregationcited by 10
  9. 2022Empirical Risk Minimization with Relative Entropy Regularization: Optimality and Sensitivity Analysiscited by 8
  10. 2021Stochastic Gradient Langevin Dynamics with Variance Reductioncited by 7
  11. 2023Smoothed f-Divergence Distributionally Robust Optimizationcited by 6
  12. 2024Equivalence of the Empirical Risk Minimization to Regularization on the Family of f-Divergencescited by 6
4 more
  1. 2024Asymmetry of the Relative Entropy in the Regularization of Empirical Risk Minimizationcited by 6
  2. 2023Information-theoretic Analysis of Test Data Sensitivity in Uncertaintycited by 3
  3. 2025Regularization via f-Divergence: An Application to Multi-Oxide Spectroscopic Analysiscited by 3
  4. 2025An Information-Theoretic Analysis for Federated Learning under Concept Driftcited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Empirical Risk Minimization with f-Divergence Regularizationcited by 0