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A Multi-Step Subgradient Algorithm for Privacy-Aware Distributed Optimization via State Decomposition
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DOI：10.1016/j.dsp.2025.105734.png)
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Abstract
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This study focuses on the privacy-aware distributed optimization problem over unbalanced directed networks, where multiple agents work together to find a global optimal solution by minimizing the sum of their local objective functions. Existing distributed subgradient-based methods, such as conventional rescaling subgradient algorithms, necessitate the explicit exchange of state values containing sensitive information, which may result in significant privacy leakage. To tackle this challenge, we introduce an efficient state-decomposition-based distributed multi-step subgradient algorithm, achieving both rapid convergence and privacy preservation. Specifically, the momentum variable and the decision variable of each agent are both divided into two sub-states: one for communication with neighbors and the other for internal iteration, ensuring that sensitive information remains undisclosed to external eavesdroppers. Additionally, a rescaling subgradient technique is employed to address the unbalancedness of the directed network. Theoretical analysis demonstrates that the proposed algorithm can achieve global optimality and ensure privacy preservation. Ultimately, numerical simulations are conducted to validate the theoretical conclusions.
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