Improving the Sample and Communication Complexity for Decentralized Non-Convex Optimization: Joint Gradient Estimation and Tracking

Jul 12, 2020

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Many modern large-scale machine learning problems benefit from decentralized and stochastic optimization. Recent works have shown that utilizing both decentralized computing and local stochastic gradient estimates can outperform state-of-the-art centralized algorithms, in applications involving highly non-convex problems, such as training deep neural networks. In this work, we propose a decentralized stochastic algorithm to deal with certain smooth non-convex problems where there are m nodes in the system, and each node has a large number of samples (denoted as n). Differently from the majority of the existing decentralized learning algorithms for either stochastic or finite-sum problems, our focus is given to both reducing the total communication rounds among the nodes, while accessing the minimum number of local data samples. In particular, we propose an algorithm named D-GET (decentralized gradient estimation and tracking), which jointly performs decentralized gradient estimation (which estimates the local gradient using a subset of local samples) and gradient tracking (which tracks the global full gradient using local estimates). We show that, to achieve certain 系 stationary solution of the deterministic finite sum problem, the proposed algorithm achieves an 饾挭(mn^1/2系^-1) sample complexity and an 饾挭(系^-1) communication complexity. These bounds significantly improve upon the best existing bounds of 饾挭(mn系^-1) and 饾挭(系^-1), respectively. Similarly, for online problems, the proposed method achieves an 饾挭(m 系^-3/2) sample complexity and an 饾挭(系^-1) communication complexity, while the best existing bounds are 饾挭(m系^-2) and 饾挭(系^-2).

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The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.

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