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A Safe-Point-Based Resilient Distributed Optimization Algorithm for Multidimensional Functions
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AI
DOI：10.1109/tsipn.2026.3748485.png)
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Abstract
En 中文
Designing a resilient algorithm for distributed optimization with a constant stepsize and multidimensional local variables is of both theoretical and practical significance in defending against attacks. To apply the algorithm to a wider range of distributed optimization scenarios, it is important to maintain a constant stepsize and no function redundancy. Thus, a key challenge is quantifying local state convergence and optimality, particularly in determining specific consensus error. To address this issue, we propose a safe-point-based resilient distributed optimization algorithm (DP-RDO), which is based on the Safe Point with Dimension Partition (SPDP). SPDP is a vector consensus strategy that uses the concept of the hyperrectangle to calculate a Safe Point. The Safe Point lies in the hyperrectangle of all normal agents that are not vulnerable to attacks. Thus, there is no need to use the time varying weight information, making the method allow for a precise expression of the consensus error bound. We further analyze the convergence of the states of all normal agents, where a Euclidean ball containing both the optimal solution and the final states of all normal agents is derived. We also thoroughly characterize their consensus error. Furthermore, we demonstrate that DP-RDO achieves linear convergence. Extensive numerical results are presented to validate the theoretical findings.
Keywords:
Resilient distributed optimization
Safe Point
Convergence error
Convergence region
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