This paper studies optimization problems over multi-agent systems, in which all agents cooperatively minimize a global objective function expressed as a sum of local cost functions. Each agent in the systems uses only local computation and communication in the overall process without leaking their private information. Based on the Barzilai–Borwein (BB) method and multi-consensus inner loops, a distributed algorithm with the availability of larger step-sizes and accelerated convergence, named as ADBB, is proposed. Moreover, owing to the employment of only row-stochastic weight matrices, ADBB can resolve the optimization problems over unbalanced directed networks without requiring the knowledge of neighbors’ out-degree for each agent. Via establishing contraction relationships between the consensus error, the optimality gap, and the gradient tracking error, ADBB is theoretically proved to converge linearly to the global optimal solution. A real-world data set is used in simulations to validate the correctness of the theoretical analysis.

本文研究了多智能体系统上的优化问题，其中所有智能体共同最小化表示为局部成本函数之和的全局目标函数。系统中的每个代理在整个过程中仅使用本地计算和通信，而不会泄漏其私有信息。基于Barzilai-Borwein（BB）方法和多共识内部循环，提出了一种具有较大步长和加速收敛性的分布式算法，称为ADBB。而且，由于仅使用行随机权重矩阵，因此ADBB可以解决不平衡有向网络上的优化问题，而无需了解每个代理的邻居出站程度。通过在共识误差，最优缺口，以及梯度跟踪误差，理论上证明了ADBB线性收敛到全局最优解。在仿真中使用真实世界的数据集来验证理论分析的正确性。