Multi-Agent Bayesian Optimization with Coupled Black-box and Affine Constraints

Wenjie Xu, Yuning Jiang, Bratislav Svetozarevic, Colin Jones

Primary Area: optimization

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Keywords: Bayesian optimization; Multi-Agent Black-box Optimization; Coupled Black-box Constraints; Coupled Affine Constraints

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TL;DR: We propose a primal-dual algorithm for distributed multi-agent Bayesian optimization with both coupled black-box constraints and known affine constraints.

Abstract: 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 $\mathcal{O}(N\sqrt{T})$ 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 $\mathcal{O}(N/\sqrt{T})$. 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.

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Submission Number: 1701