“可预测的”非凸在线点对学习的遗憾界

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中图分类号： TP301. 5 文献标志码：ADOI： 10.13705/j . issn. 1671-6841. 2023199

Abstract： Online pairwise learning is a machine learning model in which the loss functions depend on a pair of instances. Generalization is an important aspect of online pairwise learning theory research. Most of the existing works on online pairwise learning used adversarial loss functions and provided regret bounds only with convex loss functions. However， convexity was not typically applicable in practical scenarios. For non-convex online pairwise learning， the regret bound of online pairwise learning with a " predictable" loss function based on stability analysis was provided and the corresponding stability analysis was conducted. Through the relationship between stability and regret， a common way to measure the generalization ability of online pairwise learning， the regret bound was established with a " predictable" non-convex loss function. It was proved that when the learner obtained an offline oracle， " predictable" non-convex generalized online pairwise learning reached the regret bound of O（T-3/2） . This study enriched the theoretical research on non-convex online pairwise learning and was superior to the existing theoretical guarantees.

Key words： online pairwise learning; non-convex; stability; regret bounds; offline optimization oracle

0 引言

在线点对学习 主要应用于排序[ 1-3] 、度量学习[ 4] 等。（剩余11777字）