# Batch Bayesian Optimization via Particle Gradient Flows

arXiv: https://arxiv.org/abs/2209.04722 · HTML: https://mlsanity.com/paper/2209.04722/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 51 references that are in the map.
- First posted on arXiv 10 Sep 2022.

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

- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Stein Variational Gradient Descent as Gradient Flow](https://mlsanity.com/paper/1704.07520/) (2017)
- [Flow-based generative models for Markov chain Monte Carlo in lattice field theory](https://mlsanity.com/paper/1904.12072/) (2019)
- [Maximum Mean Discrepancy Gradient Flow](https://mlsanity.com/paper/1906.04370/) (2019)
- [Maximizing acquisition functions for Bayesian optimization](https://mlsanity.com/paper/1805.10196/) (2018)
- [Batch Bayesian Optimization via Local Penalization](https://mlsanity.com/paper/1505.08052/) (2015)
- [Constrained Bayesian Optimization with Noisy Experiments](https://mlsanity.com/paper/1706.07094/) (2017)
- [On the geometry of Stein variational gradient descent](https://mlsanity.com/paper/1912.00894/) (2019)
- [Sliced-Wasserstein Flows: Nonparametric Generative Modeling via Optimal Transport and Diffusions](https://mlsanity.com/paper/1806.08141/) (2018)
- [Large-Scale Wasserstein Gradient Flows](https://mlsanity.com/paper/2106.00736/) (2021)
- [The Parallel Knowledge Gradient Method for Batch Bayesian Optimization](https://mlsanity.com/paper/1606.04414/) (2016)
- [Bayesian Optimization with Gradients](https://mlsanity.com/paper/1703.04389/) (2017)
- [Parallel Bayesian Global Optimization of Expensive Functions](https://mlsanity.com/paper/1602.05149/) (2016)
- [Policy Optimization as Wasserstein Gradient Flows](https://mlsanity.com/paper/1808.03030/) (2018)
- [Parallel Predictive Entropy Search for Batch Global Optimization of Expensive Objective Functions](https://mlsanity.com/paper/1511.07130/) (2015)
- [Dynamical Optimal Transport on Discrete Surfaces](https://mlsanity.com/paper/1809.07083/) (2018)
- [Asynchronous Batch Bayesian Optimisation with Improved Local Penalisation](https://mlsanity.com/paper/1901.10452/) (2019)
- [Grassmann Stein Variational Gradient Descent](https://mlsanity.com/paper/2202.03297/) (2022)
- [Ensemble Inference Methods for Models With Noisy and Expensive Likelihoods](https://mlsanity.com/paper/2104.03384/) (2021)

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

- [Gaussian Process regression over discrete probability measures: on the non-stationarity relation between Euclidean and Wasserstein Squared Exponential Kernels](https://mlsanity.com/paper/2212.01310/) (2022)
- [Batched Energy-Entropy acquisition for Bayesian Optimization](https://mlsanity.com/paper/2410.08804/) (2024)

## Abstract (arXiv)

Bayesian Optimisation (BO) methods seek to find global optima of objective functions which are only available as a black-box or are expensive to evaluate. Such methods construct a surrogate model for the objective function, quantifying the uncertainty in that surrogate through Bayesian inference. Objective evaluations are sequentially determined by maximising an acquisition function at each step. However, this ancilliary optimisation problem can be highly non-trivial to solve, due to the non-convexity of the acquisition function, particularly in the case of batch Bayesian optimisation, where multiple points are selected in every step. In this work we reformulate batch BO as an optimisation problem over the space of probability measures. We construct a new acquisition function based on multipoint expected improvement which is convex over the space of probability measures. Practical schemes for solving this `inner' optimisation problem arise naturally as gradient flows of this objective function. We demonstrate the efficacy of this new method on different benchmark functions and compare with state-of-the-art batch BO methods.