Efficient Line Search Method Based on Regression and Uncertainty Quantification

TL;DR

This paper presents a Bayesian optimization-based line search method that leverages all available data to improve convergence and solution quality in unconstrained optimization problems, outperforming existing methods.

Contribution

It introduces a novel line search technique using Bayesian optimization that efficiently utilizes function values and gradients, enhancing exploration and solution accuracy.

Findings

Outperforms state-of-the-art methods on the CUTEst test set

Solves more problems to optimality with similar resources

Easily integrates into existing optimization frameworks

Abstract

Unconstrained optimization problems are typically solved using iterative methods, which often depend on line search techniques to determine optimal step lengths in each iteration. This paper introduces a novel line search approach. Traditional line search methods, aimed at determining optimal step lengths, often discard valuable data from the search process and focus on refining step length intervals. This paper proposes a more efficient method using Bayesian optimization, which utilizes all available data points, i.e., function values and gradients, to guide the search towards a potential global minimum. This new approach more effectively explores the search space, leading to better solution quality. It is also easy to implement and integrate into existing frameworks. Tested on the challenging CUTEst test set, it demonstrates superior performance compared to existing state-of-the-art methods, solving more problems to optimality with equivalent resource usage.