Collaborative Bayesian Optimization via Wasserstein Barycenters

2025-04-15

AI Summary

This paper addresses distributed black-box optimization by multiple agents under data privacy constraints and limited communication. Method: We propose the first privacy-preserving multi-agent Bayesian optimization framework based on the Wasserstein barycenter. Each agent locally constructs a Gaussian process (GP) surrogate model and shares only model parameters—not raw data—with peers; models are aggregated via the Wasserstein barycenter, and a novel collaborative acquisition function is designed to jointly balance exploration and privacy preservation. Contribution/Results: We establish asymptotic consistency of the proposed method. Empirical evaluation across multiple benchmark tasks shows that our approach matches the performance of centralized, non-private baselines and significantly outperforms existing collaborative Bayesian optimization methods. To the best of our knowledge, this is the first framework achieving both provably convergent and computationally efficient distributed black-box optimization under strict privacy guarantees.

Technology Category

• Search and Optimization: Distributed Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Multiagent Systems: Mechanism Design

Application Category

• Security and Privacy: Data transparency and provenance
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

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.

Problem

• Collaborative Bayesian optimization with data privacy constraints
• Integration of Gaussian process models via Wasserstein barycenters
• Balancing exploration-exploitation in decentralized function optimization

Innovation

• Collaborative BO via Wasserstein barycenters
• Shared GP models without data exchange
• Privacy-preserving centralized surrogate model