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Stochastic subgradient method converges at the rate $O(k^{-1/4})$ on weakly convex function

Damek Davis (dsd95***at***cornell.edu)
Dmitriy Drusvyatskiy (drusv***at***uw.edu)

Abstract: We prove that the projected stochastic subgradient method, applied to a weakly convex problem, drives the gradient of the Moreau envelope to zero at the rate $O(k^{-1/4})$.

Keywords: subgradient method, stochastic, Moreau envelope,

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )


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Entry Submitted: 02/08/2018
Entry Accepted: 02/08/2018
Entry Last Modified: 02/13/2018

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