Distributed optimization is a powerful paradigm to solve various problems in machine learning over networked systems. Existing first-order optimization methods perform cheap gradient descent by exchanging information per iteration only with single-hop neighbours in a network. However, in many agent networks such as sensor and robotic networks, it is prevalent that each agent can interact with other agents over multi-hop communication. Therefore, distributed optimization method over multi-hop networks is an important but overlooked topic that clearly needs to be developed. Motivated by this obs...