A Nesterov-Like Gradient Tracking Algorithm for Distributed Optimization Over Directed Networks

Qingguo Lü

doi:10.1109/TSMC.2019.2960770

2021-10-01

PRE

Qingguo Lü

廖

廖晓峰 (Xiaofeng Liao) *

Huaqing Li

Tingwen Huang

DOI：10.1109/TSMC.2019.2960770

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摘要

En 中文

In this article, we concentrate on dealing with the distributed optimization problem over a directed network, where each unit possesses its own convex cost function and the principal target is to minimize a global cost function (formulated by the average of all local cost functions) while obeying the network connectivity structure. Most of the existing methods, such as push-sum strategy, have eliminated the unbalancedness induced by the directed network via utilizing column-stochastic weights, which may be infeasible if the distributed implementation requires each unit to gain access to (at least) its out-degree information. In contrast, to be suitable for the directed networks with row-stochastic weights, we propose a new directed distributed Nesterov-like gradient tracking algorithm, named as D-DNGT, that incorporates the gradient tracking into the distributed Nesterov method with momentum terms and employs nonuniform step-sizes. D-DNGT extends a number of outstanding consensus algorithms over strongly connected directed networks. The implementation of D-DNGT is straightforward if each unit locally chooses a suitable step-size and privately regulates the weights on information that acquires from in-neighbors. If the largest step-size and the maximum momentum coefficient are positive and small sufficiently, we can prove that D-DNGT converges linearly to the optimal solution provided that the cost functions are smooth and strongly convex. We provide numerical experiments to confirm the findings in this article and contrast D-DNGT with recently proposed distributed optimization approaches.

Keyword:

Convergence

Cost function

Convex functions

Acceleration

Delays

Information processing

Directed network

distributed convex optimization

gradient tracking

linear convergence

Nesterov-like algorithm