ASYMPTOTIC NORMALITY AND OPTIMALITY IN NONSMOOTH STOCHASTIC APPROXIMATION

• 成果类型: Article
• 署名作者: Davis, Damek; Drusvyatskiy, Dmitriy; Jiang, Liwei
• 署名单位: Cornell University; University of Washington; University of Washington Seattle
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/24-AOS2401
• 发表日期: 2024
• 页码: 1485-1508
• 关键词: statistical estimators; BEHAVIOR

摘要

In their seminal work, Polyak and Juditsky showed that stochastic approximation algorithms for solving smooth equations enjoy a central limit theorem. Moreover, it has since been argued that the asymptotic covariance of the method is best possible among any estimation procedure in a local minimax sense of H & aacute;jek and Le Cam. A long-standing open question in this line of work is whether similar guarantees hold for important nonsmooth problems, such as stochastic nonlinear programming or stochastic variational inequalities. In this work, we show that this is indeed the case.