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Understanding the convergence performance of asynchronous stochastic gradientdescent method (Async-SGD) has received increasing attention in recent yearsdue to their foundational role in machine learning. To date, however, most ofthe existing works are restricted to either bounded gradient delays or convexsettings. In this paper, we focus on Async-SGD and its variant Async-SGDI(which uses increasing batch size) for non-convex optimization problems withunbounded gradient delays. We prove $o(1/\sqrt{k})$ convergence rate forAsync-SGD and $o(1/k)$ for Async-SGDI. Also, a unifying sufficient conditionfor Async-SGD's convergence is established, which includes two major gradientdelay models in the literature as special cases and yields a new delay modelnot considered thus far.

Taming Convergence for Asynchronous Stochastic Gradient Descent with Unbounded Delay in Non-Convex Learning