Geometric step decay yields local linear convergence for stochastic algorithms on sharp nonconvex problems and gives matching or new guarantees for phase retrieval and blind deconvolution under Gaussian and heavy-tailed measurements.
Let us first observe that under a very mild condition on the function f, identifiability at a critical points implies local sharp growth
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Stochastic algorithms with geometric step decay converge linearly on sharp functions
Geometric step decay yields local linear convergence for stochastic algorithms on sharp nonconvex problems and gives matching or new guarantees for phase retrieval and blind deconvolution under Gaussian and heavy-tailed measurements.