In this work, we design a distributed algorithm for time-varying convex optimization over networks with quantized communications. Each agent has its local time-varying objective function, while the agents need to cooperatively track the optimal solution trajectories of global time-varying functions. The distributed algorithm is motivated by the alternating direction method of multipliers, but the agents can only share quantization information through an undirected graph. To reduce the tracking error due to information loss in quantization, we apply the dynamic quantization scheme with a decaying scaling function. The tracking error is explicitly characterized with respect to the limit of the decaying scaling function in quantization. Furthermore, we are able to show that the algorithm could asymptotically track the optimal solution when time-varying functions converge, even with quantization information loss. Finally, the theoretical results are validated via numerical simulation.

中文翻译：

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具有动态量化的分布式时变凸优化


在这项工作中，我们设计了一种分布式算法，用于在具有量化通信的网络上进行时变凸优化。每个智能体都有其局部时变目标函数，而智能体需要合作跟踪全局时变函数的最优解轨迹。分布式算法的动机是乘法器的交替方向方法，但智能体只能通过无向图共享量化信息。为了减少由于量化中的信息丢失而导致的跟踪误差，我们应用具有衰减缩放函数的动态量化方案。跟踪误差明确地表征了量化中衰减缩放函数的极限。此外，我们还能够证明，当时变函数收敛时，即使存在量化信息丢失，该算法也可以渐近跟踪最优解。最后，通过数值模拟验证了理论结果。