# Bayesian Optimization with Gradients

arXiv: https://arxiv.org/abs/1703.04389 · HTML: https://mlsanity.com/paper/1703.04389/

## Key facts

- Cited by 59 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Mar 2017.

## Built on by (most cited first, 30 of 59)

- [Unexpected Improvements to Expected Improvement for Bayesian Optimization](https://mlsanity.com/paper/2310.20708/) (2023)
- [HPOBench: A Collection of Reproducible Multi-Fidelity Benchmark Problems for HPO](https://mlsanity.com/paper/2109.06716/) (2021)
- [PFNs4BO: In-Context Learning for Bayesian Optimization](https://mlsanity.com/paper/2305.17535/) (2023)
- [A Study of Bayesian Neural Network Surrogates for Bayesian Optimization](https://mlsanity.com/paper/2305.20028/) (2023)
- [Local policy search with Bayesian optimization](https://mlsanity.com/paper/2106.11899/) (2021)
- [Sparse Cholesky Factorization for Solving Nonlinear PDEs via Gaussian Processes](https://mlsanity.com/paper/2304.01294/) (2023)
- [Thinking inside the box: A tutorial on grey-box Bayesian optimization](https://mlsanity.com/paper/2201.00272/) (2022)
- [qEUBO: A Decision-Theoretic Acquisition Function for Preferential Bayesian Optimization](https://mlsanity.com/paper/2303.15746/) (2023)
- [A survey and benchmark of high-dimensional Bayesian optimization of discrete sequences](https://mlsanity.com/paper/2406.04739/) (2024)
- [Self-Correcting Bayesian Optimization through Bayesian Active Learning](https://mlsanity.com/paper/2304.11005/) (2023)
- [Connections and Equivalences between the Nystr"om Method and Sparse Variational Gaussian Processes](https://mlsanity.com/paper/2106.01121/) (2021)
- [High-Dimensional Gaussian Process Inference with Derivatives](https://mlsanity.com/paper/2102.07542/) (2021)
- [Scaling Gaussian Processes with Derivative Information Using Variational Inference](https://mlsanity.com/paper/2107.04061/) (2021)
- [Robust and Conjugate Gaussian Process Regression](https://mlsanity.com/paper/2311.00463/) (2023)
- [A Bayesian Optimization Framework for Finding Local Optima in Expensive Multi-Modal Functions](https://mlsanity.com/paper/2210.06635/) (2022)
- [Entropy-based adaptive design for contour finding and estimating reliability](https://mlsanity.com/paper/2105.11357/) (2021)
- [Scalable First-Order Bayesian Optimization via Structured Automatic Differentiation](https://mlsanity.com/paper/2206.08366/) (2022)
- [A portfolio approach to massively parallel Bayesian optimization](https://mlsanity.com/paper/2110.09334/) (2021)
- [Minimizing UCB: a Better Local Search Strategy in Local Bayesian Optimization](https://mlsanity.com/paper/2405.15285/) (2024)
- [Approximation-Aware Bayesian Optimization](https://mlsanity.com/paper/2406.04308/) (2024)
- [Global Optimization with Parametric Function Approximation](https://mlsanity.com/paper/2211.09100/) (2022)
- [Gaussian Max-Value Entropy Search for Multi-Agent Bayesian Optimization](https://mlsanity.com/paper/2303.05694/) (2023)
- [How to Fill the Optimum Set? Population Gradient Descent with Harmless Diversity](https://mlsanity.com/paper/2202.08376/) (2022)
- [Efficient computation of the Knowledge Gradient for Bayesian Optimization](https://mlsanity.com/paper/2209.15367/) (2022)
- [Bayesian optimization with improved scalability and derivative information for efficient design of nanophotonic structures](https://mlsanity.com/paper/2101.02972/) (2021)
- [Using Distance Correlation for Efficient Bayesian Optimization](https://mlsanity.com/paper/2102.08993/) (2021)
- [Automated Controller Calibration by Kalman Filtering](https://mlsanity.com/paper/2111.10832/) (2021)
- [Practical First-Order Bayesian Optimization Algorithms](https://mlsanity.com/paper/2306.10815/) (2023)
- [Generating Transferable Adversarial Simulation Scenarios for Self-Driving via Neural Rendering](https://mlsanity.com/paper/2309.15770/) (2023)
- [Improving Accuracy of Interpretability Measures in Hyperparameter Optimization via Bayesian Algorithm Execution](https://mlsanity.com/paper/2206.05447/) (2022)

## Abstract (arXiv)

Bayesian optimization has been successful at global optimization of expensive-to-evaluate multimodal objective functions. However, unlike most optimization methods, Bayesian optimization typically does not use derivative information. In this paper we show how Bayesian optimization can exploit derivative information to decrease the number of objective function evaluations required for good performance. In particular, we develop a novel Bayesian optimization algorithm, the derivative-enabled knowledge-gradient (dKG), for which we show one-step Bayes-optimality, asymptotic consistency, and greater one-step value of information than is possible in the derivative-free setting. Our procedure accommodates noisy and incomplete derivative information, comes in both sequential and batch forms, and can optionally reduce the computational cost of inference through automatically selected retention of a single directional derivative. We also compute the d-KG acquisition function and its gradient using a novel fast discretization-free technique. We show d-KG provides state-of-the-art performance compared to a wide range of optimization procedures with and without gradients, on benchmarks including logistic regression, deep learning, kernel learning, and k-nearest neighbors.