# Gaussian Max-Value Entropy Search for Multi-Agent Bayesian Optimization

arXiv: https://arxiv.org/abs/2303.05694 · HTML: https://mlsanity.com/paper/2303.05694/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 35 references that are in the map.
- First posted on arXiv 10 Mar 2023.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Max-value Entropy Search for Efficient Bayesian Optimization](https://mlsanity.com/paper/1703.01968/) (2017)
- [Predictive Entropy Search for Efficient Global Optimization of Black-box Functions](https://mlsanity.com/paper/1406.2541/) (2014)
- [Safe Controller Optimization for Quadrotors with Gaussian Processes](https://mlsanity.com/paper/1509.01066/) (2015)
- [The Parallel Knowledge Gradient Method for Batch Bayesian Optimization](https://mlsanity.com/paper/1606.04414/) (2016)
- [Bayesian Optimization with Gradients](https://mlsanity.com/paper/1703.04389/) (2017)
- [Parallel Gaussian Process Optimization with Upper Confidence Bound and Pure Exploration](https://mlsanity.com/paper/1304.5350/) (2013)
- [Joint Entropy Search for Multi-objective Bayesian Optimization](https://mlsanity.com/paper/2210.02905/) (2022)
- [Model-based Constrained Reinforcement Learning using Generalized Control Barrier Function](https://mlsanity.com/paper/2103.01556/) (2021)
- [Parallel Predictive Entropy Search for Batch Global Optimization of Expensive Objective Functions](https://mlsanity.com/paper/1511.07130/) (2015)
- [Joint Synthesis of Safety Certificate and Safe Control Policy using Constrained Reinforcement Learning](https://mlsanity.com/paper/2111.07695/) (2021)
- [Unbounded Bayesian Optimization via Regularization](https://mlsanity.com/paper/1508.03666/) (2015)
- [Fully Distributed Bayesian Optimization with Stochastic Policies](https://mlsanity.com/paper/1902.09992/) (2019)
- [Sim2real gap is non-monotonic with robot complexity for morphology-in-the-loop flapping wing design](https://mlsanity.com/paper/1910.13790/) (2019)
- [Distributed Information-based Source Seeking](https://mlsanity.com/paper/2209.09421/) (2022)

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

- [TS-RSR: A provably efficient approach for batch Bayesian Optimization](https://mlsanity.com/paper/2403.04764/) (2024)
- [A Unified Framework for Entropy Search and Expected Improvement in Bayesian Optimization](https://mlsanity.com/paper/2501.18756/) (2025)
- [Distributed Thompson sampling under constrained communication](https://mlsanity.com/paper/2410.15543/) (2024)
- [Information-theoretic Bayesian Optimization: Survey and Tutorial](https://mlsanity.com/paper/2502.06789/) (2025)
- [Comparing Active Learning Performance Driven by Gaussian Processes or Bayesian Neural Networks for Constrained Trajectory Exploration](https://mlsanity.com/paper/2309.16114/) (2023)
- [Multi-Agent Bayesian Optimization with Coupled Black-Box and Affine Constraints](https://mlsanity.com/paper/2310.00962/) (2023)
- [Towards safe control parameter tuning in distributed multi-agent systems](https://mlsanity.com/paper/2508.13608/) (2025)

## Abstract (arXiv)

We study the multi-agent Bayesian optimization (BO) problem, where multiple agents maximize a black-box function via iterative queries. We focus on Entropy Search (ES), a sample-efficient BO algorithm that selects queries to maximize the mutual information about the maximum of the black-box function. One of the main challenges of ES is that calculating the mutual information requires computationally-costly approximation techniques. For multi-agent BO problems, the computational cost of ES is exponential in the number of agents. To address this challenge, we propose the Gaussian Max-value Entropy Search, a multi-agent BO algorithm with favorable sample and computational efficiency. The key to our idea is to use a normal distribution to approximate the function maximum and calculate its mutual information accordingly. The resulting approximation allows queries to be cast as the solution of a closed-form optimization problem which, in turn, can be solved via a modified gradient ascent algorithm and scaled to a large number of agents. We demonstrate the effectiveness of Gaussian max-value Entropy Search through numerical experiments on standard test functions and real-robot experiments on the source-seeking problem. Results show that the proposed algorithm outperforms the multi-agent BO baselines in the numerical experiments and can stably seek the source with a limited number of noisy observations on real robots.