Delay-tolerant augmented-consensus-based distributed directed optimization

Distributed optimization finds applications in large-scale machine learning, data processing and classification over multi-agent networks. In real-world scenarios, the communication network of agents may encounter latency that may affect the convergence of the optimization protocol. This paper addresses the case where the information exchange among the agents (computing nodes) over data-transmission channels (links) might be subject to communication time-delays, which is not well addressed in the existing literature. Our proposed algorithm improves the state-of-the-art by handling heterogeneous and arbitrary but bounded and fixed (time-invariant) delays over general strongly-connected directed networks. Arguments from matrix theory, algebraic graph theory, and augmented consensus formulation are applied to prove the convergence to the optimal value. Simulations are provided to verify the results and compare the performance with some existing delay-free algorithms.