  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.
