High-Order Momentum: Improving Latency and Convergence for Wireless Network Optimization

In recent years, the rapid growth of mobile data demands has introduced many stringent requirements on latency and convergence performance in wireless network optimization. To address these challenges, several momentum-based algorithms have been proposed to improve the classical queue-length-based algorithmic framework (QLA). By combining queue-length updates and one-slot weight changes (known as the first-order momentum), it has been shown that these algorithms dramatically improve delay and convergence compared to QLA, while maintaining the same throughput-optimality and low-complexity. These exciting attempts have sparked a lot of conjectures about whether it is useful to further exploit high-order momentum information to improve delay and convergence speed. In this paper, we show that the answer is yes. Specifically, we first propose a new weight updating scheme that enables the incorporation of high-order momentum. We then prove the throughput-optimality and queue-stability of the proposed high-order momentum-based approach and characterize its delay and convergence performances. Through these analytical results, we finally show that delay and convergence would continue to improve as more high-order momentum information is utilized.