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

Code

• github.com/tkkiran/DIAG
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• github.com/POLane16/DIAG
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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.

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Reproductions