Markovian Compression: Looking to the Past Helps Accelerate the Future
Keywords: stochastic optimization, distributed optimization, compressed communications, Markovian noise
Abstract: This paper deals with distributed optimization problems that use compressed communication to achieve efficient performance and mitigate the communication bottleneck. We propose a family of compression schemes in which operators transform vectors fed to their input according to a Markov chain, i.e., the stochasticity of the compressors depends on previous iterations. Intuitively, this should accelerate the convergence of optimization methods, as considering previous iterations seems more natural and robust. The compressors are implemented in the vanilla Quantized Stochastic Gradient Descent (QSGD) algorithm. To further improve efficiency and convergence rate, we apply the momentum acceleration method. We prove convergence results for our algorithms with Markovian compressors and show theoretically that the accelerated method converges faster than the basic version. The analysis covers non-convex, Polyak-Lojasiewicz (PL), and strongly convex cases. Experiments are conducted to demonstrate the applicability of the results to distributed data-parallel optimization problems. Practical results demonstrate the superiority of methods utilizing our compressors design over several existing optimization algorithms.
Primary Area: optimization
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Submission Number: 4865
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