Improving Iterative Gaussian Processes via Warm Starting Sequential Posteriors

TL;DR

This paper introduces a novel warm-starting technique for iterative Gaussian process inference, significantly enhancing solver convergence and Bayesian optimization efficiency in sequential decision-making tasks with incremental data.

Contribution

The paper presents a new method that leverages solutions of smaller systems to accelerate convergence of iterative solvers in Gaussian process inference, improving scalability and performance.

Findings

Achieves faster convergence of iterative solvers in GP inference.

Enhances Bayesian optimization performance under fixed computational budgets.

Provides speed-ups when solving to specified tolerances.

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.