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

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