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

2025-08-28

AI Summary

We address distributed online optimization over time-varying directed networks, where existing methods often rely on bounded gradient assumptions and struggle with variance and bias induced by stochastic gradients. We propose TV-HSGT, the first algorithm to unify hybrid stochastic gradient tracking, recursive gradient estimation, and variance reduction within a time-varying directed graph framework. A novel row-column randomized communication mechanism is introduced, eliminating the need for Perron vector estimation or knowledge of node out-degrees. Theoretically, TV-HSGT achieves a dynamic regret bound of $O(sqrt{T(1+V_T)})$, improving upon state-of-the-art guarantees for comparable settings. Empirically, on dynamic resource-constrained logistic regression tasks, TV-HSGT demonstrates significantly faster convergence and enhanced stability compared to baseline methods.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Distributed Search
• Machine Learning: Online Learning & Bandits

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

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.

Problem

• Distributed online optimization in time-varying directed networks
• Overcoming reliance on bounded gradient assumptions
• Reducing gradient variance without out-degree information

Innovation

• Hybrid stochastic gradient tracking method
• Row and column stochastic communication schemes
• Variance reduction without gradient boundedness assumptions