Multi-fidelity Batch Active Learning for Gaussian Process Classifiers

2025-10-09

AI Summary

Parameter space exploration for expensive binary-output simulations poses significant challenges due to high computational cost and the intractability of mutual information computation in probability space. Method: This paper proposes a multi-fidelity batch active learning framework. Its core innovation is the Bernoulli Parameter Mutual Information (BPMI) acquisition criterion, which employs a first-order Taylor approximation to efficiently estimate mutual information—bypassing the intractable integration over the Bernoulli parameter space—and enables scalable, Bayesian-optimal sampling. The method integrates Gaussian process classifiers, multi-fidelity surrogate modeling, and batch query selection to maximize information gain under strict simulation budget constraints. Results: Evaluated on synthetic benchmarks and a real-world laser-ignition rocket combustion chamber simulation, the approach consistently outperforms state-of-the-art baselines, achieving higher predictive accuracy and faster convergence under identical simulation budgets. It provides a practical, efficient active learning framework for expensive black-box binary classification tasks.

Technology Category

• Machine Learning: Active Learning
• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Many science and engineering problems rely on expensive computational simulations, where a multi-fidelity approach can accelerate the exploration of a parameter space. We study efficient allocation of a simulation budget using a Gaussian Process (GP) model in the binary simulation output case. This paper introduces Bernoulli Parameter Mutual Information (BPMI), a batch active learning algorithm for multi-fidelity GP classifiers. BPMI circumvents the intractability of calculating mutual information in the probability space by employing a first-order Taylor expansion of the link function. We evaluate BPMI against several baselines on two synthetic test cases and a complex, real-world application involving the simulation of a laser-ignited rocket combustor. In all experiments, BPMI demonstrates superior performance, achieving higher predictive accuracy for a fixed computational budget.

Problem

• Optimizing simulation budget allocation for binary output systems
• Developing efficient multi-fidelity active learning for GP classifiers
• Solving mutual information intractability in probability space calculations

Innovation

• Multi-fidelity batch active learning for GP classifiers
• Bernoulli Parameter Mutual Information algorithm introduced
• Uses first-order Taylor expansion for tractability