[Paper Review] Multi-fidelity Bayesian Optimization with Max-value Entropy Search.

Shion Takeno, Hitoshi Fukuoka+5 more|arXiv (Cornell University)|Jan 24, 2019

Machine Learning and Data Classification18 citations

TL;DR

This paper proposes a novel multi-fidelity Bayesian optimization method using max-value entropy search (MES) to improve information gain estimation in multi-fidelity settings. By enabling analytical computation of acquisition functions with only a 1D integral and sampling, it achieves efficient and accurate optimization, demonstrating superior performance on synthetic, benchmark, and real-world materials science data.

ABSTRACT

Bayesian optimization (BO) is an effective tool for black-box optimization in which objective function evaluation is usually quite expensive. In practice, lower fidelity approximations of the objective function are often available. Recently, multi-fidelity Bayesian optimization (MFBO) has attracted considerable attention because it can dramatically accelerate the optimization process by using those cheaper observations. We propose a novel information theoretic approach to MFBO. Information-based approaches are popular and empirically successful in BO, but existing studies for information-based MFBO are plagued by difficulty for accurately estimating the information gain. Our approach is based on a variant of information-based BO called max-value entropy search (MES), which greatly facilitates evaluation of the information gain in MFBO. In fact, computations of our acquisition function is written analytically except for one dimensional integral and sampling, which can be calculated efficiently and accurately. We demonstrate effectiveness of our approach by using synthetic and benchmark datasets, and further we show a real-world application to materials science data.

Motivation & Objective

• To address the challenge of inaccurate information gain estimation in existing information-theoretic multi-fidelity Bayesian optimization (MFBO) methods.
• To improve the efficiency and accuracy of multi-fidelity optimization by leveraging a variant of entropy search tailored for multi-fidelity settings.
• To enable practical deployment of information-based MFBO by reducing computational complexity to a single 1D integral and sampling.
• To validate the method on both synthetic and real-world datasets, particularly in materials science applications.

Proposed method

• Proposes a multi-fidelity extension of max-value entropy search (MES), a variant of information-theoretic Bayesian optimization that simplifies information gain computation.
• Derives an acquisition function that enables analytical evaluation of expected information gain, except for a single one-dimensional integral.
• Uses Monte Carlo sampling to approximate the remaining 1D integral, ensuring efficient and accurate computation.
• Integrates lower-fidelity function evaluations into the optimization process to accelerate convergence toward the global optimum.
• Maintains a probabilistic model over the objective function and its fidelity levels using Gaussian processes.
• Optimizes the acquisition function to select the next evaluation point that maximizes expected information gain about the optimal input.

Experimental results

Research questions

• RQ1 Can max-value entropy search be effectively extended to multi-fidelity Bayesian optimization to improve information gain estimation?
• RQ2 How does the proposed method compare to existing MFBO approaches in terms of convergence speed and accuracy?
• RQ3 Can the method be efficiently implemented with only a single 1D integral and sampling, enabling practical deployment?
• RQ4 Does the method demonstrate strong performance on real-world materials science optimization tasks?

Key findings

• The proposed method achieves accurate information gain estimation by reformulating MES for multi-fidelity settings, reducing computational complexity to a single 1D integral.
• The acquisition function can be evaluated efficiently and accurately using sampling and analytical expressions, enabling practical use in real-world scenarios.
• Empirical results on synthetic and benchmark datasets show faster convergence and improved optimization performance compared to existing MFBO methods.
• In a real-world materials science application, the method successfully identified high-performing material compositions with fewer expensive evaluations.