Asymptotic normality and optimality in nonsmooth stochastic approximation
非光滑随机逼近中的渐近正态性与最优性
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 Hájek 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…