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Stochastic Gradient Descent (SGD) is very useful in optimization problems with high-dimensional non-convex target functions, and hence constitutes an important component of several Machine Learning and Data Analytics methods. Recently there have been significant works on understanding the parallelism inherent to SGD, and its convergence properties. Asynchronous, parallel SGD (AsyncPSGD) has received particular attention, due to observed performance benefits. On the other hand, asynchrony implies inherent challenges in understanding the execution of the algorithm and its convergence, stemming from the fact that the contribution of a thread might be based on an old (stale) view of the state. In this work we aim to deepen the understanding of AsyncPSGD in order to increase the statistical efficiency in the presence of stale gradients. We propose new models for capturing the nature of the staleness distribution in a practical setting. Using the proposed models, we derive a staleness-adaptive SGD framework, MindTheStep-AsyncPSGD, for adapting the step size in an online-fashion, which provably reduces the negative impact of asynchrony. Moreover, we provide general convergence time bounds for a wide class of staleness-adaptive step size strategies for convex target functions. We also provide a detailed empirical study, showing how our approach implies faster convergence for deep learning applications.978-1-7281-0858-2/19/$31.00 c 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

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