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.

介绍了一种新的非凸非光滑优化问题的块坐标随机梯度下降优化方法：Stochastic Asynchronous Proximal Alternating Linearized Minimization (SAPALM)，该方法在大类别的问题上是第一个能够得到收敛收敛保证的异步并行优化方法，并证明了在这个问题类别中，SAPALM 在最优异步方法或同步方法中具有相同的收敛速度，而在实践中，SAPALM 在多个矩阵分解问题上都展现出最先进的性能。