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

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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.