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Logarithmic Regret for Distributed Online Subgradient Method over Unbalanced Directed Networks
Makoto YAMASHITA Naoki HAYASHI Takeshi HATANAKA Shigemasa TAKAI
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2021/08/01
Online ISSN: 1745-1337
Type of Manuscript: PAPER
Category: Systems and Control
online optimization, multi-agent system, cooperative control, unbalanced directed network,
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This paper investigates a constrained distributed online optimization problem over strongly connected communication networks, where a local cost function of each agent varies in time due to environmental factors. We propose a distributed online projected subgradient method over unbalanced directed networks. The performance of the proposed method is evaluated by a regret which is defined by the error between the cumulative cost over time and the cost of the optimal strategy in hindsight. We show that a logarithmic regret bound can be achieved for strongly convex cost functions. We also demonstrate the validity of the proposed method through a numerical example on distributed estimation over a diffusion field.