# Amortized Acquisition Optimization for Bayesian Optimization with Variational Mutual Information

arXiv: https://arxiv.org/abs/2601.08172 · HTML: https://mlsanity.com/paper/2601.08172/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 32 references that are in the map.
- First posted on arXiv 13 Jan 2026.

## Builds on (most cited first, 20 of 20)

- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [MINE: Mutual Information Neural Estimation](https://mlsanity.com/paper/1801.04062/) (2018)
- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1402.4102/) (2014)
- [What Are Bayesian Neural Network Posteriors Really Like?](https://mlsanity.com/paper/2104.14421/) (2021)
- [Max-value Entropy Search for Efficient Bayesian Optimization](https://mlsanity.com/paper/1703.01968/) (2017)
- [Understanding the Limitations of Variational Mutual Information Estimators](https://mlsanity.com/paper/1910.06222/) (2019)
- [Dealing with Integer-valued Variables in Bayesian Optimization with Gaussian Processes](https://mlsanity.com/paper/1706.03673/) (2017)
- [Joint Entropy Search for Maximally-Informed Bayesian Optimization](https://mlsanity.com/paper/2206.04771/) (2022)
- [Predictive Entropy Search for Bayesian Optimization with Unknown Constraints](https://mlsanity.com/paper/1502.05312/) (2015)
- [A Study of Bayesian Neural Network Surrogates for Bayesian Optimization](https://mlsanity.com/paper/2305.20028/) (2023)
- [Continual Learning via Sequential Function-Space Variational Inference](https://mlsanity.com/paper/2312.17210/) (2023)
- [Accelerated Linearized Laplace Approximation for Bayesian Deep Learning](https://mlsanity.com/paper/2210.12642/) (2022)
- [Scalable Bayesian Optimization Using Vecchia Approximations of Gaussian Processes](https://mlsanity.com/paper/2203.01459/) (2022)
- [Scalable Bayesian Optimization via Focalized Sparse Gaussian Processes](https://mlsanity.com/paper/2412.20375/) (2024)
- [A Unified Framework for Entropy Search and Expected Improvement in Bayesian Optimization](https://mlsanity.com/paper/2501.18756/) (2025)
- [Pareto-frontier Entropy Search with Variational Lower Bound Maximization](https://mlsanity.com/paper/2501.19073/) (2025)
- [nuGPR: GPU-Accelerated Gaussian Process Regression with Iterative Algorithms and Low-Rank Approximations](https://mlsanity.com/paper/2510.12128/) (2025)

## Abstract (arXiv)

Bayesian optimization (BO) of expensive black-box functions is traditionally addressed with Gaussian processes (GPs), which scale cubically with observations, or Bayesian neural networks (BNNs), which incur costly posterior sampling and inner-loop acquisition optimization. We propose VBO-MI (Variational Bayesian Optimization with Mutual Information), a fully gradient-based BO framework that requires no explicit GP prior or fixed parametric posterior family over objective function and treats it as a strict black box. An actor-critic architecture pairs an action-net with a variational critic that estimates information gain, eliminating the acquisition optimization bottleneck and achieving up to 102× fewer FLOPs than BNN-BO baselines. A lightweight surrogate network further reduces real function queries to one batch per iteration. We establish consistency guarantees and evaluate VBO-MI on synthetic benchmarks (Ackley, Levy, Griewank) and real-world tasks (Rover Trajectory, Lunar Lander, Pest Control), demonstrating competitive or superior performance over the baselines.