Dynamic Distributed Convex Optimization "Over-the-Air" in Decentralized Wireless Networks

We propose a truly decentralized algorithm for solving distributed convex optimization problems with possibly time-varying objectives and dynamic networks. It is especially suitable for solving convex feasibility problems with possibly infinitely many sets, and its main novelty is that it covers practical wireless communication systems that have not been considered in previous distributed solvers. In particular, it can be used with a novel proposed protocol based on the ``over-the-air'' function computation (OTA-C) technology, which is tailored to achieve fast consensus in large and dense wireless networks. In contrast to most OTA-C protocols, the proposed protocol does not require estimates of channel statistics of individual links. Our main theoretical results establish sufficient conditions for the agents to agree on a time-invariant solution asymptotically, assuming that such a solution exists. These results are verified via simulations, where we tackle a real-world problem of distributed random field estimation in an online supervised learning framework.