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Multi-consensus Decentralized Accelerated Gradient Descent
This paper considers the decentralized optimization problem, which has
applications in large scale machine learning, sensor networks, and control
theory. We propose a novel algorithm that can achieve near optimal
communication complexity, matching the known lower bound up to a logarithmic
factor of the condition number of the problem. Our theoretical results give
affirmative answers to the open problem on whether there exists an algorithm
that can achieve a communication complexity (nearly) matching the lower bound
depending on the global condition number instead of the local one. Moreover,
the proposed algorithm achieves the optimal computation complexity matching the
lower bound up to universal constants. Furthermore, to achieve a linear
convergence rate, our algorithm \emph{doesn't} require the individual functions
to be (strongly) convex. Our method relies on a novel combination of known
techniques including Nesterov's accelerated gradient descent, multi-consensus
and gradient-tracking. The analysis is new, and may be applied to other related
problems. Empirical studies demonstrate the effectiveness of our method for
machine learning applications
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