Tootfinder

A Dual Optimization View to Empirical Risk Minimization with f-Divergence Regularization
Francisco Daunas, I\~naki Esnaola, Samir M. Perlaza
https://arxiv.org/abs/2508.03314 htt…

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

Wild Refitting for Model-Free Excess Risk Evaluation of Opaque ML/AI Models under Bregman Loss
Haichen Hu, David Simchi-Levi
https://arxiv.org/abs/2509.02476 https://

Wild Refitting for Model-Free Excess Risk Evaluation of Opaque ML/AI Models under Bregman Loss
We study the problem of evaluating the excess risk of classical penalized empirical risk minimization (ERM) with Bregman losses. We show that by leveraging the recently proposed wild refitting procedure (Wainwright, 2025), one can efficiently upper bound the excess risk through the so-called "wild optimism," without relying on the global structure of the underlying function class. This property makes our approach inherently model-free. Unlike conventional analyses, our framework operates with j…

Quantum Learning with Tunable Loss Functions
Yixian Qiu, Lirand\"e Pira, Patrick Rebentrost
https://arxiv.org/abs/2508.21369 https://arxiv.org/pdf/250…

Quantum Learning with Tunable Loss Functions
Learning from quantum data presents new challenges to the paradigm of learning from data. This typically entails the use of quantum learning models to learn quantum processes that come with enough subtleties to modify the theoretical learning frameworks. This new intersection warrants new frameworks for complexity measures, including those on quantum sample complexity and generalization bounds. Empirical risk minimization (ERM) serves as the foundational framework for evaluating learning models…

Benefits of Online Tilted Empirical Risk Minimization: A Case Study of Outlier Detection and Robust Regression
Yigit E. Yildirim, Samet Demir, Zafer Dogan
https://arxiv.org/abs/2509.15141

Benefits of Online Tilted Empirical Risk Minimization: A Case Study of Outlier Detection and Robust Regression
Empirical Risk Minimization (ERM) is a foundational framework for supervised learning but primarily optimizes average-case performance, often neglecting fairness and robustness considerations. Tilted Empirical Risk Minimization (TERM) extends ERM by introducing an exponential tilt hyperparameter $t$ to balance average-case accuracy with worst-case fairness and robustness. However, in online or streaming settings where data arrive one sample at a time, the classical TERM objective degenerates to…

Deterministic Coreset Construction via Adaptive Sensitivity Trimming
Faruk Alpay, Taylan Alpay
https://arxiv.org/abs/2508.18340 https://arxiv.org/pdf/2508.…

Deterministic Coreset Construction via Adaptive Sensitivity Trimming
We develop a rigorous framework for deterministic coreset construction in empirical risk minimization (ERM). Our central contribution is the Adaptive Deterministic Uniform-Weight Trimming (ADUWT) algorithm, which constructs a coreset by excising points with the lowest sensitivity bounds and applying a data-dependent uniform weight to the remainder. The method yields a uniform $(1\pm\varepsilon)$ relative-error approximation for the ERM objective over the entire hypothesis space. We provide comp…

Optimal differentially private kernel learning with random projection
Bonwoo Lee, Cheolwoo Park, Jeongyoun Ahn
https://arxiv.org/abs/2507.17544 https://

Optimal differentially private kernel learning with random projection
Differential privacy has become a cornerstone in the development of privacy-preserving learning algorithms. This work addresses optimizing differentially private kernel learning within the empirical risk minimization (ERM) framework. We propose a novel differentially private kernel ERM algorithm based on random projection in the reproducing kernel Hilbert space using Gaussian processes. Our method achieves minimax-optimal excess risk for both the squared loss and Lipschitz-smooth convex loss fu…