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现有分布式在线优化方法的实现通常依赖于通信网络中节点间的实时信息交换，这在实际应用中会带来无法承受的通信带宽等资源的消耗。为了减少通信成本，将边事件触发技术应用于分布式在线约束凸优化，其中每个智能体仅知晓时变的局部目标函数，所有智能体的公共目标是求解优化解序列来最小化网络总目标值（所有局部目标函数的总和）。首先，针对分布式在线梯度下降算法，在固定强连通有向图的假设下，设计了一个边事件触发机制。然后，基于所设计的边事件触发机制，为每个智能体的Regret建立了一个上界，发现该上界与事件触发阈值直接相关。进一步的分析表明，只要边事件触发阈值随着时间趋于无穷大而收敛至零时，Regret是次线性增长的。最后，通过面向时变经济调度和糖尿病分类预测问题的数值仿真实验，验证了所提出算法的有效性。
Abstract：The implementation of existing distributed online optimization methods typically relies on real-time information exchange between nodes in a communication network, which incurs unsustainable resource consumption such as communication bandwidth in practical applications. To reduce communication costs, edge-based event-triggering technology is applied to distributed online constrained convex optimization, where each agent only knows its own time-varying local objective functions, and the common goal of all agents is to calculate the optimal sequence of solutions to minimize the total network objective value(the sum of all local objective functions). Firstly, an edge-based event-triggering mechanism is designed for the distributed online gradient descent algorithm under the assumption of a fixed strongly connected directed graph. Then, based on the designed edge-based event-triggering mechanism, an upper bound for each agent′s Regret is established, which is found to be directly related to the event-triggering threshold. Further analysis reveals that as long as the edge-based event-triggering threshold converges to zero over time, the Regret exhibits sublinear growth. Finally, the effectiveness of the proposed algorithm is verified through numerical simulation experiments oriented towards time-varying economic dispatch and diabetes classification prediction problems.
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基本信息:
DOI：10.12194/j.ntu.20240110001
中图分类号:TP18
引用信息:
[1]毛帅,段冰,胡泮,等.融合边事件触发机制的分布式在线约束凸优化[J].南通大学学报(自然科学版),2024,23(03):47-58.DOI:10.12194/j.ntu.20240110001.
基金信息:
江苏省基础研究计划青年基金项目（BK20230605）; 江苏省高等学校基础科学（自然科学）研究面上项目（23KJB120011）
2024-01-10
2024
2024-02-21
2024
1
2024-02-26
2024-02-26
2024-02-26