English

Stability and Sharper Risk Bounds with Convergence Rate $\tilde{O}(1/n^2)$

Machine Learning 2025-10-31 v2 Machine Learning

Abstract

Prior work (Klochkov &\& Zhivotovskiy, 2021) establishes at most O(log(n)/n)O\left(\log (n)/n\right) excess risk bounds via algorithmic stability for strongly-convex learners with high probability. We show that under the similar common assumptions -- - Polyak-Lojasiewicz condition, smoothness, and Lipschitz continous for losses -- - rates of O(log2(n)/n2)O\left(\log^2(n)/n^2\right) are at most achievable. To our knowledge, our analysis also provides the tightest high-probability bounds for gradient-based generalization gaps in nonconvex settings.

Keywords

Cite

@article{arxiv.2410.09766,
  title  = {Stability and Sharper Risk Bounds with Convergence Rate $\tilde{O}(1/n^2)$},
  author = {Bowei Zhu and Shaojie Li and Mingyang Yi and Yong Liu},
  journal= {arXiv preprint arXiv:2410.09766},
  year   = {2025}
}