# Towards Scalable Bayesian Optimization via Gradient-Informed Bayesian Neural Networks

arXiv: https://arxiv.org/abs/2504.10076 · HTML: https://mlsanity.com/paper/2504.10076/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 26 references that are in the map.
- First posted on arXiv 14 Apr 2025.

## Builds on (most cited first, 10 of 10)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1402.4102/) (2014)
- [Neural Processes](https://mlsanity.com/paper/1807.01622/) (2018)
- [Unexpected Improvements to Expected Improvement for Bayesian Optimization](https://mlsanity.com/paper/2310.20708/) (2023)
- [Bayesian Optimization with Gradients](https://mlsanity.com/paper/1703.04389/) (2017)
- [Scaling Gaussian Process Regression with Derivatives](https://mlsanity.com/paper/1810.12283/) (2018)
- [Exploiting gradients and Hessians in Bayesian optimization and Bayesian quadrature](https://mlsanity.com/paper/1704.00060/) (2017)
- [User Preference Meets Pareto-Optimality in Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2502.06971/) (2025)

## Built on by (most cited first, 2 of 2)

- [Model-free Reinforcement Learning for Model-based Control: Towards Safe, Interpretable and Sample-efficient Agents](https://mlsanity.com/paper/2507.13491/) (2025)
- [Gradient-Informed Bayesian and Interior Point Optimization for Efficient Inverse Design in Nanophotonics](https://mlsanity.com/paper/2602.18148/) (2026)

## Abstract (arXiv)

Bayesian optimization (BO) is a widely used method for data-driven optimization that generally relies on zeroth-order data of objective function to construct probabilistic surrogate models. These surrogates guide the exploration-exploitation process toward finding global optimum. While Gaussian processes (GPs) are commonly employed as surrogates of the unknown objective function, recent studies have highlighted the potential of Bayesian neural networks (BNNs) as scalable and flexible alternatives. Moreover, incorporating gradient observations into GPs, when available, has been shown to improve BO performance. However, the use of gradients within BNN surrogates remains unexplored. By leveraging automatic differentiation, gradient information can be seamlessly integrated into BNN training, resulting in more informative surrogates for BO. We propose a gradient-informed loss function for BNN training, effectively augmenting function observations with local gradient information. The effectiveness of this approach is demonstrated on well-known benchmarks in terms of improved BNN predictions and faster BO convergence as the number of decision variables increases.