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arXiv · 2410.09766

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

Bowei Zhu·Shaojie Li·Mingyang Yi·Yong Liu
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Abstract

Prior work (Klochkov $\&$ Zhivotovskiy, 2021) establishes at most $O\left(\log (n)/n\right)$ 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 $O\left(\log^2(n)/n^2\right)$ are at most achievable. To our knowledge, our analysis also provides the tightest high-probability bounds for gradient-based generalization gaps in nonconvex settings.

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Bowei Zhu, Shaojie Li, Mingyang Yi, Yong Liu. 2024-10-13. Stability and Sharper Risk Bounds with Convergence Rate $\tilde{O}(1/n^2)$. https://arxiv.org/abs/2410.09766

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