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Stochastic Sign Descent Methods: New Algorithms and Better Theory
Mher Safaryan · Peter Richtarik

Tue Jul 20 05:20 AM -- 05:25 AM (PDT) @ None
Various gradient compression schemes have been proposed to mitigate the communication cost in distributed training of large scale machine learning models. Sign-based methods, such as signSGD (Bernstein et al., 2018), have recently been gaining popularity because of their simple compression rule and connection to adaptive gradient methods, like ADAM. In this paper, we analyze sign-based methods for non-convex optimization in three key settings: (i) standard single node, (ii) parallel with shared data and (iii) distributed with partitioned data. For single machine case, we generalize the previous analysis of signSGD relying on intuitive bounds on success probabilities and allowing even biased estimators. Furthermore, we extend the analysis to parallel setting within a parameter server framework, where exponentially fast noise reduction is guaranteed with respect to number of nodes, maintaining $1$-bit compression in both directions and using small mini-batch sizes. Next, we identify a fundamental issue with signSGD to converge in distributed environment. To resolve this issue, we propose a new sign-based method, {\em Stochastic Sign Descent with Momentum (SSDM)}, which converges under standard bounded variance assumption with the optimal asymptotic rate. We validate several aspects of our theoretical findings with numerical experiments.

#### Author Information

##### Peter Richtarik (KAUST)

Peter Richtarik is an Associate Professor of Computer Science and Mathematics at KAUST and an Associate Professor of Mathematics at the University of Edinburgh. He is an EPSRC Fellow in Mathematical Sciences, Fellow of the Alan Turing Institute, and is affiliated with the Visual Computing Center and the Extreme Computing Research Center at KAUST. Dr. Richtarik received his PhD from Cornell University in 2007, and then worked as a Postdoctoral Fellow in Louvain, Belgium, before joining Edinburgh in 2009, and KAUST in 2017. Dr. Richtarik's research interests lie at the intersection of mathematics, computer science, machine learning, optimization, numerical linear algebra, high performance computing and applied probability. Through his recent work on randomized decomposition algorithms (such as randomized coordinate descent methods, stochastic gradient descent methods and their numerous extensions, improvements and variants), he has contributed to the foundations of the emerging field of big data optimization, randomized numerical linear algebra, and stochastic methods for empirical risk minimization. Several of his papers attracted international awards, including the SIAM SIGEST Best Paper Award, the IMA Leslie Fox Prize (2nd prize, twice), and the INFORMS Computing Society Best Student Paper Award (sole runner up). He is the founder and organizer of the Optimization and Big Data workshop series.​