Collaborative Research: CIF: Small: Nonasymptotic Analysis for Stochastic Networks and Systems: Foundations and Applications

Regents Of The University Of Michigan - Ann Arbor, Ann Arbor MI

Investigators

Abstract

The confluence of cloud computing, machine learning/artificial intelligence and Internet-of-things/sensor technology is transforming society in unprecedented ways, and leading to innovations in autonomous systems, healthcare, bioinformatics, social networks, online and in-store retail industry, and education. Breakthrough developments in these widely disparate fields use machine learning and cloud computing with millions of servers to aid data-driven decision-making using terabytes of data, some in real-time and some offline. At the heart of these large-scale machine-learning and cloud-computing applications are stochastic dynamical systems of enormous scale. Analyzing and optimizing such systems are often difficult because of the size and the unknown statistical description of the underlying randomness in such systems. This project is aimed at understanding the performance of large stochastic systems by developing a new analytical method that synthesizes tools from probability, machine learning, and stochastic networks, and will lead to new advances in the design of fast and more efficient computing systems for training large-scale machine-learning models, while yielding new fundamental insights into deep reinforcement-learning algorithms. The project will contribute to education and workforce development by integrating the theories and algorithms into the graduate-level courses and by involving undergraduate and students from underrepresented groups in the research. This project develops a new analytical method for obtaining non-asymptotic bounds using Lyapunov drift analysis. The method combines drift analysis with ideas from Stein's method, dimensionality reduction from state-space collapse and properties of reproducing kernel Hilbert spaces, as appropriate. The project leverages three key ideas to advance the state-of-the-art: Stein's method to choose appropriate Lyapunov functions to study mean-field limits, identifying lower-order models using the notion of state-space collapse, and using moment-generating functions or characteristic functions as test functions to obtain higher-moment bounds on the performance of stochastic systems. During the course of this project, the method is applied to two applications: (i) robust and ultra-low latency computing networks for supporting complex machine-learning jobs with concurrent and dependent tasks, which are processed in heterogeneous server farms; and (ii) deep reinforcement-learning for deriving new performance bounds for neural temporal-difference learning and for the Actor-Critic algorithms. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.