Heavy-ball: A new approach to tame delay and convergence in wireless network optimization

The last decade has seen significant advances in optimization-based resource allocation and control approaches for wireless networks. However, the existing work suffer from poor performance in one or more of the metrics of optimality, delay, and convergence speed. To overcome these limitations, in this paper, we introduce a largely overlooked but highly effective heavy-ball optimization method. Based on this heavy-ball technique, we develop a cross-layer optimization framework that offers utility-optimality, fast-convergence, and significant delay reduction. Our contributions are three-fold: i) we propose a heavy-ball joint congestion control and routing/scheduling framework for both single-hop and multi-hop wireless networks; ii) we show that the proposed heavy-ball method offers an elegant three-way trade-off in utility, delay, and convergence, which is achieved under a near index-type simple policy; and more importantly, iii) our work opens the door to an unexplored network control and optimization paradigm that leverages advanced optimization techniques based on “memory/momentum” information.