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arXiv · 1803.09169

FROST -- Fast row-stochastic optimization with uncoordinated step-sizes

Ran Xin·Chenguang Xi·Usman A. Khan
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Abstract

In this paper, we discuss distributed optimization over directed graphs, where doubly-stochastic weights cannot be constructed. Most of the existing algorithms overcome this issue by applying push-sum consensus, which utilizes column-stochastic weights. The formulation of column-stochastic weights requires each agent to know (at least) its out-degree, which may be impractical in e.g., broadcast-based communication protocols. In contrast, we describe FROST (Fast Row-stochastic-Optimization with uncoordinated STep-sizes), an optimization algorithm applicable to directed graphs that does not require the knowledge of out-degrees; the implementation of which is straightforward as each agent locally assigns weights to the incoming information and locally chooses a suitable step-size. We show that FROST converges linearly to the optimal solution for smooth and strongly-convex functions given that the largest step-size is positive and sufficiently small.

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Ran Xin, Chenguang Xi, Usman A. Khan. 2018-11-27. FROST -- Fast row-stochastic optimization with uncoordinated step-sizes. https://doi.org/10.1186/s13634-018-0596-y

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