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In this paper, we propose the Asynchronous Accelerated Nonuniform RandomizedBlock Coordinate Descent algorithm (A2BCD), the first asynchronousNesterov-accelerated algorithm that achieves optimal complexity. This parallelalgorithm solves the unconstrained convex minimization problem, using pcomputing nodes which compute updates to shared solution vectors, in anasynchronous fashion with no central coordination. Nodes in asynchronousalgorithms do not wait for updates from other nodes before starting a newiteration, but simply compute updates using the most recent solutioninformation available. This allows them to complete iterations much faster thantraditional ones, especially at scale, by eliminating the costlysynchronization penalty of traditional algorithms.  We first prove that A2BCD converges linearly to a solution with a fastaccelerated rate that matches the recently proposed NU_ACDM, so long as themaximum delay is not too large. Somewhat surprisingly, A2BCD pays no complexitypenalty for using outdated information. We then prove lower complexity boundsfor randomized coordinate descent methods, which show that A2BCD (and henceNU_ACDM) has optimal complexity to within a constant factor. We confirm withnumerical experiments that A2BCD outperforms NU_ACDM, which is the currentfastest coordinate descent algorithm, even at small scale. We also derive andanalyze a second-order ordinary differential equation, which is thecontinuous-time limit of our algorithm, and prove it converges linearly to asolution with a similar accelerated rate.

A2BCD: An Asynchronous Accelerated Block Coordinate Descent Algorithm With Optimal Complexity