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3PC: Three Point Compressors for Communication-Efficient Distributed Training and a Better Theory for Lazy Aggregation
Peter Richtarik · Igor Sokolov · Elnur Gasanov · Ilyas Fatkhullin · Zhize Li · Eduard Gorbunov

Thu Jul 21 11:55 AM -- 12:00 PM (PDT) @ Ballroom 3 & 4

We propose and study a new class of gradient compressors for communication-efficient training---three point compressors (3PC)---as well as efficient distributed nonconvex optimization algorithms that can take advantage of them. Unlike most established approaches, which rely on a static compressor choice (e.g., TopK), our class allows the compressors to {\em evolve} throughout the training process, with the aim of improving the theoretical communication complexity and practical efficiency of the underlying methods. We show that our general approach can recover the recently proposed state-of-the-art error feedback mechanism EF21 (Richt\'{a}rik et al, 2021) and its theoretical properties as a special case, but also leads to a number of new efficient methods. Notably, our approach allows us to improve upon the state-of-the-art in the algorithmic and theoretical foundations of the {\em lazy aggregation} literature (Liu et al, 2017; Lan et al, 2017). As a by-product that may be of independent interest, we provide a new and fundamental link between the lazy aggregation and error feedback literature. A special feature of our work is that we do not require the compressors to be unbiased.

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.‚Äč

Igor Sokolov (King Abdullah University of Science and Technology)
Elnur Gasanov (KAUST)
Ilyas Fatkhullin (ETH Zurich)
Zhize Li (KAUST and CMU)
Eduard Gorbunov (Moscow Institute of Physics and Technology)

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