Asymptotic normality and optimality in nonsmooth stochastic approximation
Abstract
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 non-smooth problems, such as stochastic nonlinear programming or stochastic variational inequalities. In this work, we show that this is indeed the case.
- Publication:
-
arXiv e-prints
- Pub Date:
- January 2023
- DOI:
- 10.48550/arXiv.2301.06632
- arXiv:
- arXiv:2301.06632
- Bibcode:
- 2023arXiv230106632D
- Keywords:
-
- Mathematics - Optimization and Control;
- Mathematics - Statistics Theory;
- Statistics - Machine Learning;
- 65K05;
- 65K10;
- 90C15;
- 90C30;
- 90C06
- E-Print:
- 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