Optimal algorithms for smooth and strongly convex distributed optimization in networks

Code

• github.com/adelnabli/dadao
  pytorch★ 4

Abstract

In this paper, we determine the optimal convergence rates for strongly convex and smooth distributed optimization in two settings: centralized and decentralized communications over a network. For centralized (i.e. master/slave) algorithms, we show that distributing Nesterov's accelerated gradient descent is optimal and achieves a precision > 0 in time O(_g(1+)(1/)), where _g is the condition number of the (global) function to optimize, is the diameter of the network, and (resp. 1) is the time needed to communicate values between two neighbors (resp. perform local computations). For decentralized algorithms based on gossip, we provide the first optimal algorithm, called the multi-step dual accelerated (MSDA) method, that achieves a precision > 0 in time O(_l(1+)(1/)), where _l is the condition number of the local functions and is the (normalized) eigengap of the gossip matrix used for communication between nodes. We then verify the efficiency of MSDA against state-of-the-art methods for two problems: least-squares regression and classification by logistic regression.

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