提出黑箱方法，让非欧优化算法自动具备稳定性和最优泛化性能。
Black-Box Uniform Stability for Non-Euclidean Empirical Risk Minimization
- 利用一致凸正则项，将霍尔德光滑凸损失优化器转为统一稳定学习算法。
- 在非欧空间中实现最优统计风险界，误差仅差一个依赖p的常数因子。
- 适合研究非欧几何下的机器学习稳定性与泛化理论的人参考。
我们研究了在p-范数（p ≥ 1）下凸且光滑的经验证据风险最小化（ERM）问题中的梯度类算法的统一稳定性。提出一种黑箱归约方法，通过利用一致凸正则项的性质，将针对霍尔德光滑凸损失的优化算法转化为具有最优统计风险界（超出风险）的统一稳定学习算法，误差上界仅相差一个依赖于p的常数因子。该工作回应了Attia和Koren（2022）提出的开放问题——在非欧空间中实现黑箱统一稳定性归约，此前仅解决欧氏空间（p=2）情形。我们还探讨了利用非欧几何处理二分类问题的应用潜力。
原文摘要 · Abstract (English)
We study first-order algorithms that are uniformly stable for empirical risk minimization (ERM) problems that are convex and smooth with respect to $p$-norms, $p \geq 1$. We propose a black-box reduction method that, by employing properties of uniformly convex regularizers, turns an optimization algorithm for Hölder smooth convex losses into a uniformly stable learning algorithm with optimal statistical risk bounds on the excess risk, up to a constant factor depending on $p$. Achieving a black-box reduction for uniform stability was posed as an open question by (Attia and Koren, 2022), which had solved the Euclidean case $p=2$. We explore applications that leverage non-Euclidean geometry in addressing binary classification problems.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。