VBO-MI: A Fully Gradient-Based Bayesian Optimization Framework Using Variational Mutual Information Estimation

• URL: http://arxiv.org/abs/2601.08172v1
• Date: Tue, 13 Jan 2026 03:07:52 GMT
• Title: VBO-MI: A Fully Gradient-Based Bayesian Optimization Framework Using Variational Mutual Information Estimation
• Authors: Farhad Mirkarimi,
• Abstract summary: VBO-MI is a fully gradient-based BO framework that leverages recent advances in variational mutual information estimation.<n>We evaluate our method on a diverse suite of benchmarks, including high-dimensional synthetic functions and complex real-world tasks.
• Score: 1.0829694003408499
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Many real-world tasks require optimizing expensive black-box functions accessible only through noisy evaluations, a setting commonly addressed with Bayesian optimization (BO). While Bayesian neural networks (BNNs) have recently emerged as scalable alternatives to Gaussian Processes (GPs), traditional BNN-BO frameworks remain burdened by expensive posterior sampling and acquisition function optimization. In this work, we propose {VBO-MI} (Variational Bayesian Optimization with Mutual Information), a fully gradient-based BO framework that leverages recent advances in variational mutual information estimation. To enable end-to-end gradient flow, we employ an actor-critic architecture consisting of an {action-net} to navigate the input space and a {variational critic} to estimate information gain. This formulation effectively eliminates the traditional inner-loop acquisition optimization bottleneck, achieving up to a {$10^2 \times$ reduction in FLOPs} compared to BNN-BO baselines. We evaluate our method on a diverse suite of benchmarks, including high-dimensional synthetic functions and complex real-world tasks such as PDE optimization, the Lunar Lander control problem, and categorical Pest Control. Our experiments demonstrate that VBO-MI consistently provides the same or superior optimization performance and computational scalability over the baselines.

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