A Fully Asynchronous Newton Tracking Method for Decentralized Optimization

We consider fully asynchronous decentralized optimization over a directed graph. While various algorithms have been proposed, real-world applications require relaxing the assumption and considering communication networks with asynchronous and heterogeneous nodes. To meet these challenges, we propose an efficient and robust Newton tracking mechanism for fully asynchronous optimization. Our proposed mechanism can be adapted to different asynchronous first-order methods as required by the practical context. Through the theoretical analysis we demonstrate the R-linear rate of our method and derive an explicit expression of decaying factor under local conditions. Furthermore, numerical comparison with existing algorithms support the efficiency and robustness of our method.