Asymptotic normality and optimality in nonsmooth stochastic approximation

Damek Davis; Dmitriy Drusvyatskiy; Liwei Jiang

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arXiv · 2301.06632

Asymptotic normality and optimality in nonsmooth stochastic approximation

Damek Davis·Dmitriy Drusvyatskiy·Liwei Jiang

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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 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.

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BibTeX RIS

Damek Davis, Dmitriy Drusvyatskiy, Liwei Jiang. 2023-01-16. Asymptotic normality and optimality in nonsmooth stochastic approximation. https://arxiv.org/abs/2301.06632

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