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In this paper, we discuss distributed optimization over directed graphs,where doubly-stochastic weights cannot be constructed. Most of the existingalgorithms overcome this issue by applying push-sum consensus, which utilizescolumn-stochastic weights. The formulation of column-stochastic weightsrequires each agent to know (at least) its out-degree, which may be impracticalin e.g., broadcast-based communication protocols. In contrast, we describeFROST (Fast Row-stochastic-Optimization with uncoordinated STep-sizes), anoptimization algorithm applicable to directed graphs that does not require theknowledge of out-degrees; the implementation of which is straightforward aseach agent locally assigns weights to the incoming information and locallychooses a suitable step-size. We show that FROST converges linearly to theoptimal solution for smooth and strongly-convex functions given that thelargest step-size is positive and sufficiently small.

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