Adaptive quantized online distributed stochastic mirror descent algorithm

Online distributed optimization of multi-agent system is often used to deal with the optimization problems in dynamic environment. Considering the communication bandwidth constraints, as well as the advantages of mirror descent algorithm in processing high-dimensional data, a distributed online stochastic mirror descent algorithm with adaptive quantizer is proposed in this paper. Using the property of Bregman divergence, the quantization error and projection error of the algorithm are analyzed. When objective function is strongly convex, the regret bound of algorithm is obtained. Finally, the proposed algorithm is verified by numerical simulation.