# Conditioning Sparse Variational Gaussian Processes for Online Decision-making

arXiv: https://arxiv.org/abs/2110.15172 · HTML: https://mlsanity.com/paper/2110.15172/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 89 references that are in the map.
- First posted on arXiv 28 Oct 2021.

## Builds on (most cited first, 30 of 37)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [Scalable Variational Gaussian Process Classification](https://mlsanity.com/paper/1411.2005/) (2014)
- [Max-value Entropy Search for Efficient Bayesian Optimization](https://mlsanity.com/paper/1703.01968/) (2017)
- [Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)](https://mlsanity.com/paper/1503.01057/) (2015)
- [High-Dimensional Bayesian Optimization with Sparse Axis-Aligned Subspaces](https://mlsanity.com/paper/2103.00349/) (2021)
- [Functional Regularisation for Continual Learning with Gaussian Processes](https://mlsanity.com/paper/1901.11356/) (2019)
- [Sample-Efficient Optimization in the Latent Space of Deep Generative Models via Weighted Retraining](https://mlsanity.com/paper/2006.09191/) (2020)
- [Batched Large-scale Bayesian Optimization in High-dimensional Spaces](https://mlsanity.com/paper/1706.01445/) (2017)
- [Continual Deep Learning by Functional Regularisation of Memorable Past](https://mlsanity.com/paper/2004.14070/) (2020)
- [Constrained Bayesian Optimization with Noisy Experiments](https://mlsanity.com/paper/1706.07094/) (2017)
- [Learning Search Space Partition for Black-box Optimization using Monte Carlo Tree Search](https://mlsanity.com/paper/2007.00708/) (2020)
- [The Parallel Knowledge Gradient Method for Batch Bayesian Optimization](https://mlsanity.com/paper/1606.04414/) (2016)
- [Understanding Probabilistic Sparse Gaussian Process Approximations](https://mlsanity.com/paper/1606.04820/) (2016)
- [Conjugate-Computation Variational Inference : Converting Variational Inference in Non-Conjugate Models to Inferences in Conjugate Models](https://mlsanity.com/paper/1703.04265/) (2017)
- [Rates of Convergence for Sparse Variational Gaussian Process Regression](https://mlsanity.com/paper/1903.03571/) (2019)
- [Deep Gaussian Processes for Multi-fidelity Modeling](https://mlsanity.com/paper/1903.07320/) (2019)
- [Streaming Variational Bayes](https://mlsanity.com/paper/1307.6769/) (2013)
- [Constant-Time Predictive Distributions for Gaussian Processes](https://mlsanity.com/paper/1803.06058/) (2018)
- [GIBBON: General-purpose Information-Based Bayesian OptimisatioN](https://mlsanity.com/paper/2102.03324/) (2021)
- [Meta Reinforcement Learning with Latent Variable Gaussian Processes](https://mlsanity.com/paper/1803.07551/) (2018)
- [Streaming Sparse Gaussian Process Approximations](https://mlsanity.com/paper/1705.07131/) (2017)
- [Efficient Nonmyopic Bayesian Optimization via One-Shot Multi-Step Trees](https://mlsanity.com/paper/2006.15779/) (2020)
- [Variational Auto-Regressive Gaussian Processes for Continual Learning](https://mlsanity.com/paper/2006.05468/) (2020)
- [Bayesian Optimization using Deep Gaussian Processes](https://mlsanity.com/paper/1905.03350/) (2019)

## Built on by (most cited first, 23 of 23)

- [Accelerating Bayesian Optimization for Biological Sequence Design with Denoising Autoencoders](https://mlsanity.com/paper/2203.12742/) (2022)
- [Multi-Objective GFlowNets](https://mlsanity.com/paper/2210.12765/) (2022)
- [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)
- [Bayesian Optimization with Conformal Prediction Sets](https://mlsanity.com/paper/2210.12496/) (2022)
- [Multi-Fidelity Active Learning with GFlowNets](https://mlsanity.com/paper/2306.11715/) (2023)
- [Scalable Bayesian Optimization Using Vecchia Approximations of Gaussian Processes](https://mlsanity.com/paper/2203.01459/) (2022)
- [Memory-Based Dual Gaussian Processes for Sequential Learning](https://mlsanity.com/paper/2306.03566/) (2023)
- [Approximation-Aware Bayesian Optimization](https://mlsanity.com/paper/2406.04308/) (2024)
- [Scalable Bayesian Optimization via Focalized Sparse Gaussian Processes](https://mlsanity.com/paper/2412.20375/) (2024)
- [Fantasizing with Dual GPs in Bayesian Optimization and Active Learning](https://mlsanity.com/paper/2211.01053/) (2022)
- [Advancing Deep Active Learning & Data Subset Selection: Unifying Principles with Information-Theory Intuitions](https://mlsanity.com/paper/2401.04305/) (2024)
- [Fast post-process Bayesian inference with Variational Sparse Bayesian Quadrature](https://mlsanity.com/paper/2303.05263/) (2023)
- [Weighted Ensembles for Active Learning with Adaptivity](https://mlsanity.com/paper/2206.05009/) (2022)
- [BatchGFN: Generative Flow Networks for Batch Active Learning](https://mlsanity.com/paper/2306.15058/) (2023)
- [Recurrent Memory for Online Interdomain Gaussian Processes](https://mlsanity.com/paper/2502.08736/) (2025)
- [Robust, Online, and Adaptive Decentralized Gaussian Processes](https://mlsanity.com/paper/2509.18011/) (2025)
- [Volatility Based Kernels and Moving Average Means for Accurate Forecasting with Gaussian Processes](https://mlsanity.com/paper/2207.06544/) (2022)
- [Adjusting Model Size in Continual Gaussian Processes: How Big is Big Enough?](https://mlsanity.com/paper/2408.07588/) (2024)
- [Robust and Computation-Aware Gaussian Processes](https://mlsanity.com/paper/2505.21133/) (2025)
- [Streaming PAC-Bayes Gaussian process regression with a performance guarantee for online decision making](https://mlsanity.com/paper/2210.08486/) (2022)
- [Exact and general decoupled solutions of the LMC Multitask Gaussian Process model](https://mlsanity.com/paper/2310.12032/) (2023)
- [Fast Gaussian process inference by exact Mat'ern kernel decomposition](https://mlsanity.com/paper/2508.01864/) (2025)

## Abstract (arXiv)

With a principled representation of uncertainty and closed form posterior updates, Gaussian processes (GPs) are a natural choice for online decision making. However, Gaussian processes typically require at least O(n2) computations for n training points, limiting their general applicability. Stochastic variational Gaussian processes (SVGPs) can provide scalable inference for a dataset of fixed size, but are difficult to efficiently condition on new data. We propose online variational conditioning (OVC), a procedure for efficiently conditioning SVGPs in an online setting that does not require re-training through the evidence lower bound with the addition of new data. OVC enables the pairing of SVGPs with advanced look-ahead acquisition functions for black-box optimization, even with non-Gaussian likelihoods. We show OVC provides compelling performance in a range of applications including active learning of malaria incidence, and reinforcement learning on MuJoCo simulated robotic control tasks.