Stochastic Learning of Computational Resource Usage as Graph Structured Multimarginal Schr\"odinger Bridge

TL;DR

This paper introduces a novel nonparametric method to learn and predict the time-varying stochastic distribution of computational resource usage in software, using a graph-structured Schrödinger bridge framework.

Contribution

It develops a new stochastic learning approach for joint modeling of correlated, time-varying computational resources as a Schrödinger bridge problem, with algorithms and guarantees.

Findings

Effective in predicting resource availability distributions.

Applicable to single-core and multi-core systems.

Demonstrated in case studies with nonlinear control and synthetic software.

Abstract

We propose to learn the time-varying stochastic computational resource usage of software as a graph structured Schr\"odinger bridge problem. In general, learning the computational resource usage from data is challenging because resources such as the number of CPU instructions and the number of last level cache requests are both time-varying and statistically correlated. Our proposed method enables learning the joint time-varying stochasticity in computational resource usage from the measured profile snapshots in a nonparametric manner. The method can be used to predict the most-likely time-varying distribution of computational resource availability at a desired time. We provide detailed algorithms for stochastic learning in both single and multi-core cases, discuss the convergence guarantees, computational complexities, and demonstrate their practical use in two case studies: a single-core nonlinear model predictive controller, and a synthetic multi-core software.