Broadcast-based asynchronous convex optimization using quantized distributed stochastic mirror descent algorithm

We investigate a distributed convex optimization problem associated with a multi-agent network in this paper. Considering that there is no central coordinator in the network, each agent can only send information to its neighbors. For this case, a broadcast scheme based on asynchronous communication is adopted in this paper. Moreover, due to the limitation of network communication bandwidth, time-varying quantizers are used in data exchange. Then a broadcast-based quantized distributed stochastic mirror descent (B-QDSMD) algorithm is developed to solve the distributed convex optimization problem in the non-Euclidean sense. The performance of the algorithm with constant step size is also analyzed. It can be proved that the convergence of the algorithm is influenced by the selection of quantization solutions and step sizes for each agent. We also provide numerical examples to illustrate the applicability of the proposed algorithm.