Stochastic Learning of Computational Resource Usage as Graph Structured Multimarginal Schrödinger Bridge

2024-05-21

arXiv.org

AI Summary

This work addresses the challenge of modeling time-varying, non-stationary, and multidimensional stochastic resource usage in software systems—such as CPU instruction counts and last-level cache requests. We propose a nonparametric joint temporal distribution learning method. Our core innovation is the first formulation of resource evolution as a graph-structured multi-marginal Schrödinger bridge problem, integrating optimal transport theory, graph neural operators, and stochastic process inference to jointly learn time-varying distributions and predict most probable resource trajectories from sparse performance snapshots. The method inherently encodes multi-core scheduling constraints and guarantees theoretical convergence with parallel scalability. Evaluated on a single-core nonlinear model predictive control (MPC) benchmark and a synthetic multi-core system, our approach achieves a 32% improvement in temporal distribution fitting accuracy over state-of-the-art baselines and enables real-time, resource-aware scheduling.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Virtualization and resource management in Web systems and infrastructures
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• Learn time-varying stochastic computational resource usage
• Model statistically correlated CPU and cache resources
• Predict most-likely resource availability distributions

Innovation

• Learn computational resource usage via Schrödinger bridge
• Nonparametric learning from measured profile snapshots
• Predict time-varying resource distribution accurately