Accelerated Stochastic Gradient Method with Applications to Consensus Problem in Markov-Varying Networks

Stochastic optimization is a vital field in the realm of mathematical optimization, finding applications in diverse domains ranging from operations research to machine learning. In this paper, we introduce a novel first-order optimization algorithm designed for scenarios where Markovian noise is present, incorporating Nesterov acceleration for enhanced efficiency. The convergence analysis is performed by using an assumption on noise depending on the distance to the solution. We also delve into the consensus problem over Markov-varying networks, exploring how this algorithm can be applied to achieve agreement among multiple agents with differing objectives during the changes into communication system. To show the performance of our method on the problem above, we conduct experiments to demonstrate the superiority over the classic approach.