Asymptotic normality and optimality in nonsmooth stochastic approximation

Autor:	Davis, Damek, Drusvyatskiy, Dmitriy, Jiang, Liwei
Rok vydání:	2023
Předmět:	Mathematics - Optimization and Control Mathematics - Statistics Theory Statistics - Machine Learning 65K05 65K10 90C15 90C30 90C06
Druh dokumentu:	Working Paper
Popis:	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\'{a}jek and Le Cam. A long-standing open question in this line of work is whether similar guarantees hold for important non-smooth problems, such as stochastic nonlinear programming or stochastic variational inequalities. In this work, we show that this is indeed the case. Comment: The arxiv report arXiv:2108.11832 has been split into two parts. This is Part 2 of the original submission, augmented by a some new results and a reworked exposition
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2301.06632 Zobrazit plný text záznamu View this record from Arxiv