CIF: Small: Taming Convergence and Delay in Stochastic Network Optimization with Hessian Information

随着大量数据和新网络设备的快速集成，当今的网络基础设施正在扩展到其极限。因此，近年来已经见证了一个关键的需求，发展快速收敛的分布式随机网络控制和优化算法，以增加吞吐量和减少延迟。该研究计划解决了下一代复杂网络系统的分布式控制和优化的挑战，其中快速变化的网络状态（例如，网络拓扑、信道状态、接入状态等）在分布式优化算法中需要快速收敛和低延迟。基于研究者最近对利用二阶Hessian信息（SOHI）的网络控制和优化的研究，本研究将开发一系列新的分布式算法技术，与传统方法相比，这些技术在收敛速度和延迟方面都有数量级的改进，同时达到相同的可证明网络效用最优性。具体来说，调查员？的研究任务在这个项目中组织围绕三个相互关联的研究重点，利用不同程度的SOHI：i）重球为基础的联合拥塞控制和多路径路由（部分SOHI）; ii）原始-对偶通道点二阶拥塞控制和多路径路由（全SOHI）;和iii）基于SOHI的分布式控制和优化算法设计。该研究项目采用综合和整体的方法，从数学建模，优化理论，控制理论，嵌入式理论和随机分析领域汲取技术。该研究项目不仅将推进下一代复杂网络算法设计的知识，还将通过探索基于SOI的网络控制和优化的新前沿，满足一般网络研究社区的关键需求。

With the rapid integration of massive amounts of data and new network devices, today's network infrastructures are being stretched to their limits. As a result, recent years have witnessed a critical need for developing fast-converging distributed stochastic network control and optimization algorithms to increase throughput and reduce delay. This research program addresses the challenge of distributed control and optimization for next generation complex network systems, where the rapidly changing network states (e.g., network topologies, channel states, queueing states, etc.) necessitate fast-convergence and low-delay in distributed optimization algorithms. Based on the investigator's recent research on network control and optimization that leverages second-order Hessian information (SOHI), this research will develop a series of new distributed algorithmic techniques that offer orders of magnitudes improvements in both convergence speed and queueing delay compared to the traditional approaches, while attaining the same provable network-utility optimality. Specifically, the investigator?s research tasks in this project are organized around three inter-related research thrusts that exploit different degrees of SOHI: i) Heavy-ball-based joint congestion control and multi-path routing (partial SOHI); ii) Primal-dual interior-point second-order congestion control and multi-path routing (full SOHI); and iii) SOHI-based distributed control and optimization algorithm designs. This research project takes an integrated and holistic approach that draws techniques from areas of mathematical modeling, optimization theory, control theory, queueing theory, and stochastic analysis. The research project will not only advance the knowledge in the algorithmic design for next generation complex networks, but will also serve a critical need in the general networking research community by exploring new frontiers in SOHI-based network control and optimization.