Distributed Time-Varying Convex Optimization With Dynamic Quantization

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.

Automated summary

In this work, a distributed algorithm is proposed for time-varying convex optimization over networks with quantized communications. The algorithm utilizes dynamic quantization scheme to reduce information loss, and it is capable of asymptotically tracking the optimal solution even with quantization information loss, as validated by theoretical analysis and numerical simulation.