Distributed Online Optimization under Dynamic Adaptive Quantization

For distributed online optimization over networked nodes, we propose an algorithm based on one-step gradient descent and multi-step consensus under dynamic adaptive quantization. We propose a dynamic difference encoding-decoding strategy with variable center quantizers and online-generated quantization intervals, which adjust the quantization parameters adaptively according to the optimizers' states. We use the fixed gradient descent step size to ensure the ability of tracking the optimal solutions of the dynamically changing objective functions, and give the upper bound of the dynamic regret. The effectiveness of the proposed algorithm is demonstrated by numerical simulation.