# Multi-Agent Bayesian Optimization with Coupled Black-Box and Affine Constraints

arXiv: https://arxiv.org/abs/2310.00962 · HTML: https://mlsanity.com/paper/2310.00962/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 46 references that are in the map.
- First posted on arXiv 2 Oct 2023.

## Builds on (most cited first, 22 of 22)

- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [On Information Gain and Regret Bounds in Gaussian Process Bandits](https://mlsanity.com/paper/2009.06966/) (2020)
- [High Dimensional Bayesian Optimisation and Bandits via Additive Models](https://mlsanity.com/paper/1503.01673/) (2015)
- [Parallel Bayesian Optimization of Multiple Noisy Objectives with Expected Hypervolume Improvement](https://mlsanity.com/paper/2105.08195/) (2021)
- [Bayesian Optimization with Unknown Constraints](https://mlsanity.com/paper/1403.5607/) (2014)
- [Online Convex Optimization with Stochastic Constraints](https://mlsanity.com/paper/1708.03741/) (2017)
- [The Parallel Knowledge Gradient Method for Batch Bayesian Optimization](https://mlsanity.com/paper/1606.04414/) (2016)
- [What Doubling Tricks Can and Can't Do for Multi-Armed Bandits](https://mlsanity.com/paper/1803.06971/) (2018)
- [High-Dimensional Bayesian Optimization via Additive Models with Overlapping Groups](https://mlsanity.com/paper/1802.07028/) (2018)
- [Constrained Efficient Global Optimization of Expensive Black-box Functions](https://mlsanity.com/paper/2211.00162/) (2022)
- [Provably Efficient Model-Free Constrained RL with Linear Function Approximation](https://mlsanity.com/paper/2206.11889/) (2022)
- [On Kernelized Multi-Armed Bandits with Constraints](https://mlsanity.com/paper/2203.15589/) (2022)
- [VABO: Violation-Aware Bayesian Optimization for Closed-Loop Control Performance Optimization with Unmodeled Constraints](https://mlsanity.com/paper/2110.07479/) (2021)
- [Rectified Pessimistic-Optimistic Learning for Stochastic Continuum-armed Bandit with Constraints](https://mlsanity.com/paper/2211.14720/) (2022)
- [Gaussian Max-Value Entropy Search for Multi-Agent Bayesian Optimization](https://mlsanity.com/paper/2303.05694/) (2023)
- [Violation-Aware Contextual Bayesian Optimization for Controller Performance Optimization with Unmodeled Constraints](https://mlsanity.com/paper/2301.12099/) (2023)
- [Hierarchical Multi-Agent Optimization for Resource Allocation in Cloud Computing](https://mlsanity.com/paper/2001.03929/) (2020)
- [A Probabilistic Approach for Demand-Aware Ride-Sharing Optimization](https://mlsanity.com/paper/1905.00084/) (2019)
- [Dissipativity in economic model predictive control: beyond steady-state optimality](https://mlsanity.com/paper/1911.09908/) (2019)
- [Optimizing Two-Truck Platooning with Deadlines](https://mlsanity.com/paper/2210.01889/) (2022)
- [Multi-agent Black-box Optimization using a Bayesian Approach to Alternating Direction Method of Multipliers](https://mlsanity.com/paper/2303.14414/) (2023)

## Abstract (arXiv)

This paper studies the problem of distributed multi-agent Bayesian optimization with both coupled black-box constraints and known affine constraints. A primal-dual distributed algorithm is proposed that achieves similar regret/violation bounds as those in the single-agent case for the black-box objective and constraint functions. Additionally, the algorithm guarantees an O(N√T) bound on the cumulative violation for the known affine constraints, where N is the number of agents. Hence, it is ensured that the average of the samples satisfies the affine constraints up to the error O(N/√T). Furthermore, we characterize certain conditions under which our algorithm can bound a stronger metric of cumulative violation and provide best-iterate convergence without affine constraint. The method is then applied to both sampled instances from Gaussian processes and a real-world optimal power allocation problem for wireless communication; the results show that our method simultaneously provides close-to-optimal performance and maintains minor violations on average, corroborating our theoretical analysis.