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The Sound of APALM Clapping: Faster Nonsmooth Nonconvex Optimization with Stochastic Asynchronous PALM

Damek Davis · Brent Edmunds · Madeleine Udell

Area 5+6+7+8 #51

Keywords: [ Stochastic Methods ] [ (Other) Optimization ] [ Convex Optimization ] [ Large Scale Learning and Big Data ] [ Matrix Factorization ]


We introduce the Stochastic Asynchronous Proximal Alternating Linearized Minimization (SAPALM) method, a block coordinate stochastic proximal-gradient method for solving nonconvex, nonsmooth optimization problems. SAPALM is the first asynchronous parallel optimization method that provably converges on a large class of nonconvex, nonsmooth problems. We prove that SAPALM matches the best known rates of convergence --- among synchronous or asynchronous methods --- on this problem class. We provide upper bounds on the number of workers for which we can expect to see a linear speedup, which match the best bounds known for less complex problems, and show that in practice SAPALM achieves this linear speedup. We demonstrate state-of-the-art performance on several matrix factorization problems.

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