An Asynchronous Parallel Stochastic Coordinate Descent Algorithm

We describe an asynchronous parallel stochastic coordinate descent algorithm for minimizing smooth unconstrained or separably constrained functions. The method achieves a linear convergence rate on functions that satisfy an essential strong convexity property and a sublinear rate ($1\mathrm{/}K$) on general convex functions. Near-linear speedup on a multicore system can be expected if the number of processors is $O(n^{1\mathrm{/}2})$ in unconstrained optimization and $O(n^{1\mathrm{/}4})$ in the separable-constrained case, where $n$ is the number of variables. We describe results from implementation on 40-core processors.