A Generalized Framework of Multifidelity Max-Value Entropy Search Through Joint Entropy

Area of Science:

• Computational Mathematics
• Machine Learning
• Optimization

Background:

• Bayesian optimization (BO) is effective for expensive black-box problems but can be slow.
• Multifidelity Bayesian optimization (MFBO) uses cheaper, lower-fidelity data to accelerate BO.
• Existing multifidelity max-value entropy search (MF-MES) is limited to sequential single observations.

Purpose of the Study:

• Generalize MF-MES to handle simultaneous multifidelity observations.
• Enable synchronous parallelization and trace-aware querying in MFBO.
• Maintain computational simplicity and practical effectiveness of MF-MES.

Main Methods:

• Extended the information-theoretic approach of MF-MES.
• Developed acquisition functions for simultaneous querying without new assumptions.
• Provided computational techniques for entropy evaluation and posterior sampling.

Main Results:

• The generalized MF-MES effectively handles synchronous parallelization and trace-aware querying.
• Acquisition functions retain the simplicity of the original MF-MES.
• Demonstrated effectiveness on benchmark functions and real-world applications.

Conclusions:

• The generalized MF-MES significantly enhances the efficiency of multifidelity Bayesian optimization.
• The method is broadly applicable to accelerating complex optimization tasks.
• This work advances MFBO for practical applications in science and machine learning.