Asynchronous Parallel Nonconvex Optimization Under the Polyak-Łojasiewicz Condition

Communication delays and synchronization are major bottlenecks for parallel computing, tolerating asynchrony is therefore crucial accelerating computation. Motivated by optimization problems that do not satisfy convexity assumptions, we present an asynchronous block coordinate descent algorithm nonconvex whose objective functions the Polyak-Łojasiewicz condition. This condition a generalization of strong to requires neither nor uniqueness minimizers. Under only assumptions mild smoothness bounded delays, prove linear convergence rate obtained. Numerical experiments logistic regression presented illustrate impact upon convergence.