# Diversified Sampling for Batched Bayesian Optimization with Determinantal Point Processes

arXiv: https://arxiv.org/abs/2110.11665 · HTML: https://mlsanity.com/paper/2110.11665/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 35 references that are in the map.
- First posted on arXiv 22 Oct 2021.

## Builds on (most cited first, 15 of 15)

- [A Tutorial on Thompson Sampling](https://mlsanity.com/paper/1707.02038/) (2017)
- [Learning to Optimize Via Posterior Sampling](https://mlsanity.com/paper/1301.2609/) (2013)
- [Batch Bayesian Optimization via Local Penalization](https://mlsanity.com/paper/1505.08052/) (2015)
- [Lower Bounds on Regret for Noisy Gaussian Process Bandit Optimization](https://mlsanity.com/paper/1706.00090/) (2017)
- [Adaptive and Safe Bayesian Optimization in High Dimensions via One-Dimensional Subspaces](https://mlsanity.com/paper/1902.03229/) (2019)
- [Parallel Gaussian Process Optimization with Upper Confidence Bound and Pure Exploration](https://mlsanity.com/paper/1304.5350/) (2013)
- [Batched Gaussian Process Bandit Optimization via Determinantal Point Processes](https://mlsanity.com/paper/1611.04088/) (2016)
- [Perturbed-History Exploration in Stochastic Linear Bandits](https://mlsanity.com/paper/1903.09132/) (2019)
- [Optimal Transport Kernels for Sequential and Parallel Neural Architecture Search](https://mlsanity.com/paper/2006.07593/) (2020)
- [Monte Carlo Markov Chain Algorithms for Sampling Strongly Rayleigh Distributions and Determinantal Point Processes](https://mlsanity.com/paper/1602.05242/) (2016)
- [Bayesian Optimization for Synthetic Gene Design](https://mlsanity.com/paper/1505.01627/) (2015)
- [Bayesian experimental design using regularized determinantal point processes](https://mlsanity.com/paper/1906.04133/) (2019)
- [Fast DPP Sampling for Nystr"om with Application to Kernel Methods](https://mlsanity.com/paper/1603.06052/) (2016)
- [Convergence Analysis of Block Coordinate Algorithms with Determinantal Sampling](https://mlsanity.com/paper/1910.11561/) (2019)
- [Sensing Cox Processes via Posterior Sampling and Positive Bases](https://mlsanity.com/paper/2110.11181/) (2021)

## Built on by (most cited first, 24 of 24)

- [Inducing Point Allocation for Sparse Gaussian Processes in High-Throughput Bayesian Optimisation](https://mlsanity.com/paper/2301.10123/) (2023)
- [Sample-Then-Optimize Batch Neural Thompson Sampling](https://mlsanity.com/paper/2210.06850/) (2022)
- [Quality-Weighted Vendi Scores And Their Application To Diverse Experimental Design](https://mlsanity.com/paper/2405.02449/) (2024)
- [SnAKe: Bayesian Optimization with Pathwise Exploration](https://mlsanity.com/paper/2202.00060/) (2022)
- [Pareto Front-Diverse Batch Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2406.08799/) (2024)
- [Batch Bayesian Optimization for Replicable Experimental Design](https://mlsanity.com/paper/2311.01195/) (2023)
- [SOBER: Highly Parallel Bayesian Optimization and Bayesian Quadrature over Discrete and Mixed Spaces](https://mlsanity.com/paper/2301.11832/) (2023)
- [Thompson Sampling via Fine-Tuning of LLMs](https://mlsanity.com/paper/2510.13328/) (2025)
- [Nonmyopic Multiclass Active Search with Diminishing Returns for Diverse Discovery](https://mlsanity.com/paper/2202.03593/) (2022)
- [TS-RSR: A provably efficient approach for batch Bayesian Optimization](https://mlsanity.com/paper/2403.04764/) (2024)
- [A Quadrature Approach for General-Purpose Batch Bayesian Optimization via Probabilistic Lifting](https://mlsanity.com/paper/2404.12219/) (2024)
- [On Regret Bounds of Thompson Sampling for Bayesian Optimization](https://mlsanity.com/paper/2603.09276/) (2026)
- [Optimal Initialization of Batch Bayesian Optimization](https://mlsanity.com/paper/2404.17997/) (2024)
- [Batched Bayesian optimization by maximizing the probability of including the optimum](https://mlsanity.com/paper/2410.06333/) (2024)
- [Multi-fidelity batch Bayesian optimization for bioprocess development across scales](https://mlsanity.com/paper/2508.10970/) (2025)
- [Randomized Kriging Believer for Parallel Bayesian Optimization with Regret Bounds](https://mlsanity.com/paper/2603.01470/) (2026)
- [A Guide to Bayesian Optimization in Bioprocess Engineering](https://mlsanity.com/paper/2508.10642/) (2025)
- [Batched Stochastic Linear Bandits with 1-Bit Communication Constraints](https://mlsanity.com/paper/2605.30976/) (2026)
- [Improved Regret Analysis for Parallel Gaussian Process Bandit Optimization](https://mlsanity.com/paper/2608.16492/) (2026)
- [Scalable Batch Bayesian Optimization Via Subspace Acquisition Functions](https://mlsanity.com/paper/2411.16206/) (2024)
- [Adaptive Quality-Diversity Trade-offs for Large-Scale Batch Recommendation](https://mlsanity.com/paper/2602.02024/) (2026)
- [Building informative materials datasets beyond targeted objectives](https://mlsanity.com/paper/2605.05104/) (2026)
- [Towards Regret Guarantees for One-Step Lookahead Bayesian Optimization](https://mlsanity.com/paper/2606.00956/) (2026)
- [B3O: Scalable Boltzmann Batch Bayesian Optimization](https://mlsanity.com/paper/2606.30228/) (2026)

## Abstract (arXiv)

In Bayesian Optimization (BO) we study black-box function optimization with noisy point evaluations and Bayesian priors. Convergence of BO can be greatly sped up by batching, where multiple evaluations of the black-box function are performed in a single round. The main difficulty in this setting is to propose at the same time diverse and informative batches of evaluation points. In this work, we introduce DPP-Batch Bayesian Optimization (DPP-BBO), a universal framework for inducing batch diversity in sampling based BO by leveraging the repulsive properties of Determinantal Point Processes (DPP) to naturally diversify the batch sampling procedure. We illustrate this framework by formulating DPP-Thompson Sampling (DPP-TS) as a variant of the popular Thompson Sampling (TS) algorithm and introducing a Markov Chain Monte Carlo procedure to sample from it. We then prove novel Bayesian simple regret bounds for both classical batched TS as well as our counterpart DPP-TS, with the latter bound being tighter. Our real-world, as well as synthetic, experiments demonstrate improved performance of DPP-BBO over classical batching methods with Gaussian process and Cox process models.