Achieving Low-Delay and Fast-Convergence in Stochastic Network Optimization

Abstract

Due to the rapid growth of mobile data demands, there have been significant interests in stochastic resource control and optimization for wireless networks. Although significant advances have been made in stochastic network optimization theory, to date, most of the existing approaches are plagued by either slow convergence or unsatisfactory delay performances. To address these challenges, in this paper, we develop a new stochastic network optimization framework inspired by the Nesterov accelerated gradient method. We show that our proposed Nesterovian approach offers utility-optimality, fast-convergence, and significant delay reduction in stochastic network optimization. Our contributions in this paper are threefold: i) we propose a Nesterovian joint congestion control and routing/scheduling framework for both single-hop and multi-hop wireless networks; ii) we establish the utility optimality and queueing stability of the proposed Nesterovian method, and analytically characterize its delay reduction and convergence speed; and iii) we show that the proposed Nesterovian approach offers a three-way performance control between utility-optimality, delay, and convergence.

Towards Fast-Convergence, Low-Delay and Low-Complexity Network Optimization

“…Theorem 1 says that our proposed algorithm achieves optimal utility while guaranteeing that the physical queue length at each node is a finite constant. This result improves the utility-delay tradeoffs of prior works including [7], [8]. All these methods will produce an unbounded queue length to obtain a vanishing utility optimality gap.…”

“…In the QCA method, the scheduling component is the classical MaxWeight scheduling, and the objective function is linear and such a problem can be reduced to some classical combinatorial problems such as maximum weighted matching. Instead, in our scheduling component (8), the objective function is quadratic, and the optimal solution may not belong to the vertex set Γ of the convex hull C, which poses a significant challenge in solving this problem. However, utilizing the idea of ellipsoid method, we will show a surprising result that the complexity of solving our new scheduling component ( 8) is equivalent to the complexity of solving the traditional MaxWeight scheduling problem.…”

“…tradeoff produced by recent momentum-based methods [7], [8]. Due to the nonsmoothness of dual function and the subgradient nature, all the above methods suffer from a slow convergence that requires O(1/ 2 ) iterations to obtain an −accurate solution.…”

A Theory of Second-Order Wireless Network Optimization and Its Application on AoI

“…Hence, we have µ 1 = m {1} and σ 2 1 = v 2 {1} . Given, p 1 , q 1 , and λ 1 , we can combine (4), (5), and ( 14) to obtain a theoretical approximation of the AoI. We note that (5) involves a summation of infinite terms…”

“…Techniques based on dual decomposition, Lyapunov function, etc., have been shown to produce tractable and optimal solutions in complex networks for a wide range of objectives, including maximizing spectrum efficiency, minimizing power consumption, enforcing fairness among clients, and the combination of these objectives. Recent studies have also established iterative algorithms that not only converge to the optimum, but also have provably fast convergence rate [1]- [5]. On the other hand, there have been growing interests in new performance metrics for emerging network applications, such as quality-ofexperience (QoE) for the application of video streaming and age-of-information (AoI) for the application of real-time state estimation.…”