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

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Publication date: 8 February 2018

Abstract: We prove that the proximal 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})

. As a consequence, we resolve an open question on the convergence rate of the proximal stochastic gradient method for minimizing the sum of a smooth nonconvex function and a convex proximable function.

Has companion code repository: https://github.com/tkkiran/DIAG

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