# Fantasizing with Dual GPs in Bayesian Optimization and Active Learning

arXiv: https://arxiv.org/abs/2211.01053 · HTML: https://mlsanity.com/paper/2211.01053/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 23 references that are in the map.
- First posted on arXiv 2 Nov 2022.

## Builds on (most cited first, 16 of 16)

- [Scalable Variational Gaussian Process Classification](https://mlsanity.com/paper/1411.2005/) (2014)
- [Maximizing acquisition functions for Bayesian optimization](https://mlsanity.com/paper/1805.10196/) (2018)
- [The Bayesian Learning Rule](https://mlsanity.com/paper/2107.04562/) (2021)
- [The Parallel Knowledge Gradient Method for Batch Bayesian Optimization](https://mlsanity.com/paper/1606.04414/) (2016)
- [Conjugate-Computation Variational Inference : Converting Variational Inference in Non-Conjugate Models to Inferences in Conjugate Models](https://mlsanity.com/paper/1703.04265/) (2017)
- [GIBBON: General-purpose Information-Based Bayesian OptimisatioN](https://mlsanity.com/paper/2102.03324/) (2021)
- [Streaming Sparse Gaussian Process Approximations](https://mlsanity.com/paper/1705.07131/) (2017)
- [Scalable Thompson Sampling using Sparse Gaussian Process Models](https://mlsanity.com/paper/2006.05356/) (2020)
- [Conditioning Sparse Variational Gaussian Processes for Online Decision-making](https://mlsanity.com/paper/2110.15172/) (2021)
- [Multiobjective optimization using Gaussian process emulators via stepwise uncertainty reduction](https://mlsanity.com/paper/1310.0732/) (2013)
- [Fast Variational Learning in State-Space Gaussian Process Models](https://mlsanity.com/paper/2007.04731/) (2020)
- [Dual Parameterization of Sparse Variational Gaussian Processes](https://mlsanity.com/paper/2111.03412/) (2021)
- [Bayesian Quantile and Expectile Optimisation](https://mlsanity.com/paper/2001.04833/) (2020)
- [BOSH: Bayesian Optimization by Sampling Hierarchically](https://mlsanity.com/paper/2007.00939/) (2020)
- [Information-theoretic Inducing Point Placement for High-throughput Bayesian Optimisation](https://mlsanity.com/paper/2206.02437/) (2022)
- [A penalisation method for batch multi-objective Bayesian optimisation with application in heat exchanger design](https://mlsanity.com/paper/2206.13326/) (2022)

## Built on by (most cited first, 7 of 7)

- [GAUCHE: A Library for Gaussian Processes in Chemistry](https://mlsanity.com/paper/2212.04450/) (2022)
- [Inducing Point Allocation for Sparse Gaussian Processes in High-Throughput Bayesian Optimisation](https://mlsanity.com/paper/2301.10123/) (2023)
- [Return of the Latent Space COWBOYS: Re-thinking the use of VAEs for Bayesian Optimisation of Structured Spaces](https://mlsanity.com/paper/2507.03910/) (2025)
- [Trieste: Efficiently Exploring The Depths of Black-box Functions with TensorFlow](https://mlsanity.com/paper/2302.08436/) (2023)
- [Memory-Based Dual Gaussian Processes for Sequential Learning](https://mlsanity.com/paper/2306.03566/) (2023)
- [MONGOOSE: Path-wise Smooth Bayesian Optimisation via Meta-learning](https://mlsanity.com/paper/2302.11533/) (2023)
- [In-Context Multi-Objective Optimization](https://mlsanity.com/paper/2512.11114/) (2025)

## Abstract (arXiv)

Gaussian processes (GPs) are the main surrogate functions used for sequential modelling such as Bayesian Optimization and Active Learning. Their drawbacks are poor scaling with data and the need to run an optimization loop when using a non-Gaussian likelihood. In this paper, we focus on `fantasizing' batch acquisition functions that need the ability to condition on new fantasized data computationally efficiently. By using a sparse Dual GP parameterization, we gain linear scaling with batch size as well as one-step updates for non-Gaussian likelihoods, thus extending sparse models to greedy batch fantasizing acquisition functions.