分析随机坐标下降在配对学习中的泛化能力，给出理论保障。
Stability-based Generalization Analysis of Randomized Coordinate Descent for Pairwise Learning
- 基于平均输入稳定性分析RCD的泛化行为
- 在低噪声下实现最优阶O(1/n)的过拟合误差界
- 适用于关注理论保证的优化与学习研究者
配对学习涵盖多种机器学习任务，排名和度量学习是其主要代表。尽管随机坐标下降（RCD）在各类学习问题中广泛应用，但针对其在配对学习框架下的泛化行为的理论分析仍很匮乏。本文研究了RCD在配对学习中的泛化性能，基于凸与强凸目标函数的平均输入稳定性，推导出期望意义上的泛化界。采用早停策略量化估计与优化之间的平衡，并将低噪声设定引入过剩风险界，获得$O(1/n)$的乐观界，其中$n$为样本量。
原文摘要 · Abstract (English)
Pairwise learning includes various machine learning tasks, with ranking and metric learning serving as the primary representatives. While randomized coordinate descent (RCD) is popular in various learning problems, there is much less theoretical analysis on the generalization behavior of models trained by RCD, especially under the pairwise learning framework. In this paper, we consider the generalization of RCD for pairwise learning. We measure the on-average argument stability for both convex and strongly convex objective functions, based on which we develop generalization bounds in expectation. The early-stopping strategy is adopted to quantify the balance between estimation and optimization. Our analysis further incorporates the low-noise setting into the excess risk bound to achieve the optimistic bound as $O(1/n)$, where $n$ is the sample size.
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