Fast Distributed Gradient Methods

Details Fast Distributed Gradient Methods Fast Distributed Gradient Methods

2011-12-13

arxiv.org/abs/1112.2972v1

Computer Science

Information Theory

32 pages, journal, submitted Nov 30, 2011

Scientific paper

The paper proposes new fast distributed optimization gradient methods and proves convergence to the exact solution at rate O(\log k/k), much faster than existing distributed optimization (sub)gradient methods with convergence O(1/\sqrt{k}), while incurring practically no additional communication nor computation cost overhead per iteration. We achieve this for convex (with at least one strongly convex,) coercive, three times differentiable and with Lipschitz continuous first derivative (private) cost functions. Our work recovers for distributed optimization similar convergence rate gains obtained by centralized Nesterov gradient and fast iterative shrinkage-thresholding algorithm (FISTA) methods over ordinary centralized gradient methods. We also present a constant step size distributed fast gradient algorithm for composite non-differentiable costs. A simulation illustrates the effectiveness of our distributed methods.

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