ARock: an Algorithmic Framework for Asynchronous Parallel Coordinate Updates
This provides a scalable solution for parallel computing in scientific and machine learning applications, though it is incremental as it builds on existing coordinate update methods.
The authors tackled the problem of finding fixed points of nonexpansive operators, which arises in areas like optimization and machine learning, by proposing ARock, an asynchronous parallel coordinate update framework that reduces synchronization and communication bottlenecks, and they showed it converges to fixed points with probability one and linear convergence under weaker conditions than prior work.
Finding a fixed point to a nonexpansive operator, i.e., $x^*=Tx^*$, abstracts many problems in numerical linear algebra, optimization, and other areas of scientific computing. To solve fixed-point problems, we propose ARock, an algorithmic framework in which multiple agents (machines, processors, or cores) update $x$ in an asynchronous parallel fashion. Asynchrony is crucial to parallel computing since it reduces synchronization wait, relaxes communication bottleneck, and thus speeds up computing significantly. At each step of ARock, an agent updates a randomly selected coordinate $x_i$ based on possibly out-of-date information on $x$. The agents share $x$ through either global memory or communication. If writing $x_i$ is atomic, the agents can read and write $x$ without memory locks. Theoretically, we show that if the nonexpansive operator $T$ has a fixed point, then with probability one, ARock generates a sequence that converges to a fixed points of $T$. Our conditions on $T$ and step sizes are weaker than comparable work. Linear convergence is also obtained. We propose special cases of ARock for linear systems, convex optimization, machine learning, as well as distributed and decentralized consensus problems. Numerical experiments of solving sparse logistic regression problems are presented.