# Collaborative Bayesian Optimization via Wasserstein Barycenters

arXiv: https://arxiv.org/abs/2504.10770 · HTML: https://mlsanity.com/paper/2504.10770/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 54 references that are in the map.
- First posted on arXiv 15 Apr 2025.

## Builds on (most cited first, 30 of 31)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Federated Learning with Non-IID Data](https://mlsanity.com/paper/1806.00582/) (2018)
- [Statistical Aspects of Wasserstein Distances](https://mlsanity.com/paper/1806.05500/) (2018)
- [Multi-fidelity Bayesian Optimisation with Continuous Approximations](https://mlsanity.com/paper/1703.06240/) (2017)
- [Parallel Bayesian Optimization of Multiple Noisy Objectives with Expected Hypervolume Improvement](https://mlsanity.com/paper/2105.08195/) (2021)
- [Batched Large-scale Bayesian Optimization in High-dimensional Spaces](https://mlsanity.com/paper/1706.01445/) (2017)
- [Federated Accelerated Stochastic Gradient Descent](https://mlsanity.com/paper/2006.08950/) (2020)
- [Bayesian optimization for materials design](https://mlsanity.com/paper/1506.01349/) (2015)
- [Federated Bayesian Optimization via Thompson Sampling](https://mlsanity.com/paper/2010.10154/) (2020)
- [The Parallel Knowledge Gradient Method for Batch Bayesian Optimization](https://mlsanity.com/paper/1606.04414/) (2016)
- [Parallel Bayesian Global Optimization of Expensive Functions](https://mlsanity.com/paper/1602.05149/) (2016)
- [Preference Exploration for Efficient Bayesian Optimization with Multiple Outcomes](https://mlsanity.com/paper/2203.11382/) (2022)
- [Robust Multi-Objective Bayesian Optimization Under Input Noise](https://mlsanity.com/paper/2202.07549/) (2022)
- [FedADMM: A Federated Primal-Dual Algorithm Allowing Partial Participation](https://mlsanity.com/paper/2203.15104/) (2022)
- [Parallel Predictive Entropy Search for Batch Global Optimization of Expensive Objective Functions](https://mlsanity.com/paper/1511.07130/) (2015)
- [Hybrid Random Features](https://mlsanity.com/paper/2110.04367/) (2021)
- [A supermartingale approach to Gaussian process based sequential design of experiments](https://mlsanity.com/paper/1608.01118/) (2016)
- [Procrustes Metrics on Covariance Operators and Optimal Transportation of Gaussian Processes](https://mlsanity.com/paper/1801.01990/) (2018)
- [Multi-Step Budgeted Bayesian Optimization with Unknown Evaluation Costs](https://mlsanity.com/paper/2111.06537/) (2021)
- [Meta-Learning Linear Quadratic Regulators: A Policy Gradient MAML Approach for Model-free LQR](https://mlsanity.com/paper/2401.14534/) (2024)
- [Learning Prediction Intervals for Regression: Generalization and Calibration](https://mlsanity.com/paper/2102.13625/) (2021)
- [Scalable Bayesian Optimization Using Vecchia Approximations of Gaussian Processes](https://mlsanity.com/paper/2203.01459/) (2022)
- [Collaborative and Distributed Bayesian Optimization via Consensus: Showcasing the Power of Collaboration for Optimal Design](https://mlsanity.com/paper/2306.14348/) (2023)
- [Demystifying Orthogonal Monte Carlo and Beyond](https://mlsanity.com/paper/2005.13590/) (2020)
- [Coreset-Based Task Selection for Sample-Efficient Meta-Reinforcement Learning](https://mlsanity.com/paper/2502.02332/) (2025)
- [Differential Privacy of Aggregated DC Optimal Power Flow Data](https://mlsanity.com/paper/1903.11237/) (2019)
- [Knowledge Gradient for Selection with Covariates: Consistency and Computation](https://mlsanity.com/paper/1906.05098/) (2019)
- [Pseudo-Bayesian Optimization](https://mlsanity.com/paper/2310.09766/) (2023)
- [Distributed Thompson sampling under constrained communication](https://mlsanity.com/paper/2410.15543/) (2024)

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

- [SOCRATES: Simulation Optimization with Correlated Replicas and Adaptive Trajectory Evaluations](https://mlsanity.com/paper/2511.00685/) (2025)
- [Collaborative Contextual Bayesian Optimization](https://mlsanity.com/paper/2604.18912/) (2026)
- [Demystifying Manifold Constraints in LLM Pre-training](https://mlsanity.com/paper/2605.04418/) (2026)
- [ARCO-BO: Adaptive Resource-aware COllaborative Bayesian Optimization for Heterogeneous Multi-Agent Design](https://mlsanity.com/paper/2510.16652/) (2025)
- [Weighted Wasserstein Barycenter of Gaussian Processes for exotic Bayesian Optimization tasks](https://mlsanity.com/paper/2602.09181/) (2026)
- [Privacy-Aware Collaborative and Distributed Bayesian Optimization](https://mlsanity.com/paper/2607.11600/) (2026)
- [GUIDE-FBO: Guidance via Uncertainty Intervention and Distributional Exchange for Federated Bayesian Optimization](https://mlsanity.com/paper/2609.35038/) (2026)

## Abstract (arXiv)

Motivated by the growing need for black-box optimization and data privacy, we introduce a collaborative Bayesian optimization (BO) framework that addresses both of these challenges. In this framework agents work collaboratively to optimize a function they only have oracle access to. In order to mitigate against communication and privacy constraints, agents are not allowed to share their data but can share their Gaussian process (GP) surrogate models. To enable collaboration under these constraints, we construct a central model to approximate the objective function by leveraging the concept of Wasserstein barycenters of GPs. This central model integrates the shared models without accessing the underlying data. A key aspect of our approach is a collaborative acquisition function that balances exploration and exploitation, allowing for the optimization of decision variables collaboratively in each iteration. We prove that our proposed algorithm is asymptotically consistent and that its implementation via Monte Carlo methods is numerically accurate. Through numerical experiments, we demonstrate that our approach outperforms other baseline collaborative frameworks and is competitive with centralized approaches that do not consider data privacy.