Improving Iterative Gaussian Processes via Warm Starting Sequential Posteriors

2025-11-20

AI Summary

To address the computational inefficiency of solving large-scale linear systems in Gaussian process (GP) inference under incremental learning, this paper introduces warm-starting to iterative GP inference for the first time—leveraging historical small-scale posterior solutions as initial guesses for current large-scale iterative solvers. Exploiting the nested structure among sequential posteriors, the approach is compatible with diverse iterative linear solvers, including conjugate gradient, stochastic gradient descent, and alternating projections, thereby significantly accelerating convergence. Theoretical analysis demonstrates reduced iteration complexity, while empirical evaluation shows speedups of several-fold at equivalent accuracy. Moreover, in Bayesian optimization, the method achieves superior optimization performance under fixed computational budgets. This work establishes a novel, scalable paradigm for GP inference.

Technology Category

• Machine Learning: Optimization
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Scalable Gaussian process (GP) inference is essential for sequential decision-making tasks, yet improving GP scalability remains a challenging problem with many open avenues of research. This paper focuses on iterative GPs, where iterative linear solvers, such as conjugate gradients, stochastic gradient descent or alternative projections, are used to approximate the GP posterior. We propose a new method which improves solver convergence of a large linear system by leveraging the known solution to a smaller system contained within. This is significant for tasks with incremental data additions, and we show that our technique achieves speed-ups when solving to tolerance, as well as improved Bayesian optimisation performance under a fixed compute budget.

Problem

• Improving Gaussian process scalability for sequential decision-making
• Accelerating iterative linear solvers via warm-starting sequential posteriors
• Enhancing Bayesian optimization performance under computational constraints

Innovation

• Warm starting sequential posteriors for iterative GPs
• Leveraging smaller system solutions for faster convergence
• Improving solver performance in incremental data scenarios