Asymptotic normality and optimality in nonsmooth stochastic approximation

• URL: http://arxiv.org/abs/2301.06632v1
• Date: Mon, 16 Jan 2023 23:17:47 GMT
• Title: Asymptotic normality and optimality in nonsmooth stochastic approximation
• Authors: Damek Davis, Dmitriy Drusvyatskiy, Liwei Jiang
• Abstract summary: In their seminal work, Polyak and Juditsky showed that approximation for solving smooth equations enjoy a central limit. A long-standing open question in this line of work is whether similar guarantees hold for important non-smooth problems.
• Score: 8.805688232946471
• License: http://creativecommons.org/licenses/by/4.0/
• 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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