# Batch Bayesian Optimization for Replicable Experimental Design

arXiv: https://arxiv.org/abs/2311.01195 · HTML: https://mlsanity.com/paper/2311.01195/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 45 references that are in the map.
- First posted on arXiv 2 Nov 2023.

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

- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [Max-value Entropy Search for Efficient Bayesian Optimization](https://mlsanity.com/paper/1703.01968/) (2017)
- [Biological Sequence Design with GFlowNets](https://mlsanity.com/paper/2203.04115/) (2022)
- [Batched Large-scale Bayesian Optimization in High-dimensional Spaces](https://mlsanity.com/paper/1706.01445/) (2017)
- [Batch Bayesian Optimization via Local Penalization](https://mlsanity.com/paper/1505.08052/) (2015)
- [Re-Examining Linear Embeddings for High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2001.11659/) (2020)
- [Federated Bayesian Optimization via Thompson Sampling](https://mlsanity.com/paper/2010.10154/) (2020)
- [Information Directed Sampling and Bandits with Heteroscedastic Noise](https://mlsanity.com/paper/1801.09667/) (2018)
- [The Parallel Knowledge Gradient Method for Batch Bayesian Optimization](https://mlsanity.com/paper/1606.04414/) (2016)
- [Adversarially Robust Optimization with Gaussian Processes](https://mlsanity.com/paper/1810.10775/) (2018)
- [No-Regret Bayesian Optimization with Unknown Hyperparameters](https://mlsanity.com/paper/1901.03357/) (2019)
- [Parallel Gaussian Process Optimization with Upper Confidence Bound and Pure Exploration](https://mlsanity.com/paper/1304.5350/) (2013)
- [Bayesian Optimization of Risk Measures](https://mlsanity.com/paper/2007.05554/) (2020)
- [Differentially Private Federated Bayesian Optimization with Distributed Exploration](https://mlsanity.com/paper/2110.14153/) (2021)
- [On Lower Bounds for Standard and Robust Gaussian Process Bandit Optimization](https://mlsanity.com/paper/2008.08757/) (2020)
- [Replication or exploration? Sequential design for stochastic simulation experiments](https://mlsanity.com/paper/1710.03206/) (2017)
- [Sample-Then-Optimize Batch Neural Thompson Sampling](https://mlsanity.com/paper/2210.06850/) (2022)
- [Diversified Sampling for Batched Bayesian Optimization with Determinantal Point Processes](https://mlsanity.com/paper/2110.11665/) (2021)
- [Value-at-Risk Optimization with Gaussian Processes](https://mlsanity.com/paper/2105.06126/) (2021)
- [Mean-Variance Analysis in Bayesian Optimization under Uncertainty](https://mlsanity.com/paper/2009.08166/) (2020)
- [Risk-averse Heteroscedastic Bayesian Optimization](https://mlsanity.com/paper/2111.03637/) (2021)
- [Federated Neural Bandits](https://mlsanity.com/paper/2205.14309/) (2022)
- [Scaling Gaussian Process Optimization by Evaluating a Few Unique Candidates Multiple Times](https://mlsanity.com/paper/2201.12909/) (2022)
- [On Batch Bayesian Optimization](https://mlsanity.com/paper/1911.01032/) (2019)
- [Quantum Bayesian Optimization](https://mlsanity.com/paper/2310.05373/) (2023)
- [Achieving Robustness to Aleatoric Uncertainty with Heteroscedastic Bayesian Optimisation](https://mlsanity.com/paper/1910.07779/) (2019)
- [Bayesian Optimization under Stochastic Delayed Feedback](https://mlsanity.com/paper/2206.09341/) (2022)
- [Exploiting correlation and budget constraints in Bayesian multi-armed bandit optimization](https://mlsanity.com/paper/1303.6746/) (2013)

## Built on by (most cited first, 8 of 8)

- [Quantum Lipschitz Bandits](https://mlsanity.com/paper/2504.02251/) (2025)
- [A Quadrature Approach for General-Purpose Batch Bayesian Optimization via Probabilistic Lifting](https://mlsanity.com/paper/2404.12219/) (2024)
- [PIED: Physics-Informed Experimental Design for Inverse Problems](https://mlsanity.com/paper/2503.07070/) (2025)
- [Anchor-Based Heteroscedastic Noise for Preferential Bayesian Optimization](https://mlsanity.com/paper/2405.14657/) (2024)
- [A Guide to Bayesian Optimization in Bioprocess Engineering](https://mlsanity.com/paper/2508.10642/) (2025)
- [Weighted Euclidean Distance Matrices over Mixed Continuous and Categorical Inputs for Gaussian Process Models](https://mlsanity.com/paper/2503.02630/) (2025)
- [Efficient Heteroscedastic Bayesian Optimization for Risk-Aware AutoRL](https://mlsanity.com/paper/2607.26680/) (2026)
- [Principled Design of Expected Improvement for Continuous Simulation Optimization](https://mlsanity.com/paper/2610.18434/) (2026)

## Abstract (arXiv)

Many real-world experimental design problems (a) evaluate multiple experimental conditions in parallel and (b) replicate each condition multiple times due to large and heteroscedastic observation noise. Given a fixed total budget, this naturally induces a trade-off between evaluating more unique conditions while replicating each of them fewer times vs. evaluating fewer unique conditions and replicating each more times. Moreover, in these problems, practitioners may be risk-averse and hence prefer an input with both good average performance and small variability. To tackle both challenges, we propose the Batch Thompson Sampling for Replicable Experimental Design (BTS-RED) framework, which encompasses three algorithms. Our BTS-RED-Known and BTS-RED-Unknown algorithms, for, respectively, known and unknown noise variance, choose the number of replications adaptively rather than deterministically such that an input with a larger noise variance is replicated more times. As a result, despite the noise heteroscedasticity, both algorithms enjoy a theoretical guarantee and are asymptotically no-regret. Our Mean-Var-BTS-RED algorithm aims at risk-averse optimization and is also asymptotically no-regret. We also show the effectiveness of our algorithms in two practical real-world applications: precision agriculture and AutoML.