  Distributed nonconvex optimization problems underlie many applications in
learning 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 an
uncoordinated stepsize selection rule for partially asynchronous block
coordinate descent that only requires local information to implement, and it
leads to faster convergence for a class of nonconvex problems than existing
stepsize rules, which require global information in some form. The problems we
consider satisfy the error bound condition, and the stepsize rule we present
only requires each agent to know (i) a certain type of Lipschitz constant of
its block of the gradient of the objective and (ii) the communication delays
experienced between it and its neighbors. This formulation requires less
information to be available to each agent than existing approaches, typically
allows for agents to use much larger stepsizes, and alleviates the impact of
stragglers while still guaranteeing convergence to a stationary point.
Simulation results provide comparisons and validate the faster convergence
attained by the stepsize rule we develop.
