A Hybrid Stochastic Gradient Tracking Method for Distributed Online Optimization Over Time-Varying Directed Networks

• URL: http://arxiv.org/abs/2508.20645v1
• Date: Thu, 28 Aug 2025 10:47:18 GMT
• Title: A Hybrid Stochastic Gradient Tracking Method for Distributed Online Optimization Over Time-Varying Directed Networks
• Authors: Xinli Shi, Xingxing Yuan, Longkang Zhu, Guanghui Wen,
• Abstract summary: This study proposes a novel Time-Varying Hybrid Gradient Tracking algorithm named TV-HSGT.<n>TV-HSGT integrates row-stochastic and column-stochastic communication schemes over time-varying digraphs.<n>It effectively reduces variance while accurately tracking global descent directions.
• Score: 12.821275204894635
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: With the increasing scale and dynamics of data, distributed online optimization has become essential for real-time decision-making in various applications. However, existing algorithms often rely on bounded gradient assumptions and overlook the impact of stochastic gradients, especially in time-varying directed networks. This study proposes a novel Time-Varying Hybrid Stochastic Gradient Tracking algorithm named TV-HSGT, based on hybrid stochastic gradient tracking and variance reduction mechanisms. Specifically, TV-HSGT integrates row-stochastic and column-stochastic communication schemes over time-varying digraphs, eliminating the need for Perron vector estimation or out-degree information. By combining current and recursive stochastic gradients, it effectively reduces gradient variance while accurately tracking global descent directions. Theoretical analysis demonstrates that TV-HSGT can achieve improved bounds on dynamic regret without assuming gradient boundedness. Experimental results on logistic regression tasks confirm the effectiveness of TV-HSGT in dynamic and resource-constrained environments.

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