GENERALIZATION ANALYSIS FOR CVaR-BASED MINIMAX REGRET OPTIMIZATION  

基于条件风险价值的极小极大遗憾优化的泛化分析

作　　者：TAO Yan-fang DENG Hao 陶艳芳;邓昊(武汉商学院信息工程学院,湖北武汉430056;华中农业大学信息学院,湖北武汉430070)

机构地区：[1]School of Information Engineering,Wuhan Business University,Wuhan 430056,China [2]College of Informatics,Huazhong Agricultural University,Wuhan 430070,China

出　　处：《数学杂志》2025年第2期111-121,共11页Journal of Mathematics

基　　金：Supported by Education Science Planning Project of Hubei Province(2020GB198);Natural Science Foundation of Hubei Province(2023AFB523).

摘　　要：This paper analyzes the generalization of minimax regret optimization(MRO)under distribution shift.A new learning framework is proposed by injecting the measure of con-ditional value at risk(CVaR)into MRO,and its generalization error bound is established through the lens of uniform convergence analysis.The CVaR-based MRO can achieve the polynomial decay rate on the excess risk,which extends the generalization analysis associated with the expected risk to the risk-averse case.本文研究了分布漂移情形下极小极大遗憾优化(minimax regretoptimization,MRO)的泛化性分析问题.通过引入条件风险价值(conditional valueatrisk,CVaR)这一度量提出了一种新的学习框架,并从一致收敛分析的角度建立了其泛化误差界,实现了超额风险的多项式衰减率,将期望风险相关的泛化分析扩展到风险规避情形.

关 键 词：Minimax regret optimization(MRO) conditional value at risk(CVaR) distri-bution shift generalization error 

分 类 号：O29[理学—应用数学]