提出非凸优化中更优的泛化误差界，收敛速度达1/n²。
Stability and Sharper Risk Bounds with Convergence Rate $\tilde{O}(1/n^2)$
- 在PL条件等常见假设下，改进泛化误差上界
- 高概率下实现O(log²n/n²)的收敛速率
- 适用于梯度类学习器，适合理论研究者
先前工作（Klochkov & Zhivotovskiy, 2021）在强凸学习器下，通过算法稳定性建立了最多O(log n/n)的过剩风险上界。本文在类似常见假设——Polyak-Lojasiewicz条件、光滑性及损失函数Lipschitz连续——下，证明O(log²n/n²)的上界是可达到的。据我们所知，该分析也为非凸设置中基于梯度的泛化差距提供了最紧的高概率界。
原文摘要 · Abstract (English)
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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