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Distributed nonconvex optimization problems underlie many applications inlearning and autonomy, and such problems commonly face asynchrony in agents'computations and communications. When delays in these operations are bounded,they are called partially asynchronous. In this paper, we present anuncoordinated stepsize selection rule for partially asynchronous blockcoordinate descent that only requires local information to implement, and itleads to faster convergence for a class of nonconvex problems than existingstepsize rules, which require global information in some form. The problems weconsider satisfy the error bound condition, and the stepsize rule we presentonly requires each agent to know (i) a certain type of Lipschitz constant ofits block of the gradient of the objective and (ii) the communication delaysexperienced between it and its neighbors. This formulation requires lessinformation to be available to each agent than existing approaches, typicallyallows for agents to use much larger stepsizes, and alleviates the impact ofstragglers while still guaranteeing convergence to a stationary point.Simulation results provide comparisons and validate the faster convergenceattained by the stepsize rule we develop.

Faster Asynchronous Nonconvex Block Coordinate Descent with Locally Chosen Stepsizes