  Understanding the convergence performance of asynchronous stochastic gradient
descent method (Async-SGD) has received increasing attention in recent years
due to their foundational role in machine learning. To date, however, most of
the existing works are restricted to either bounded gradient delays or convex
settings. In this paper, we focus on Async-SGD and its variant Async-SGDI
(which uses increasing batch size) for non-convex optimization problems with
unbounded gradient delays. We prove $o(1/\sqrt{k})$ convergence rate for
Async-SGD and $o(1/k)$ for Async-SGDI. Also, a unifying sufficient condition
for Async-SGD's convergence is established, which includes two major gradient
delay models in the literature as special cases and yields a new delay model
not considered thus far.
