How can we efficiently gather information to optimize an unknown function,
when presented with multiple, mutually dependent information sources with
different costs? For example, when optimizing a robotic system, intelligently
trading off computer simulations and real robot testings can lead to
significant savings. Existing methods, such as multi-fidelity GP-UCB or Entropy
Search-based approaches, either make simplistic assumptions on the interaction
among different fidelities or use simple heuristics that lack theoretical
guarantees. In this paper, we study multi-fidelity Bayesian optimization with
complex structural dependencies among multiple outputs, and propose
MF-MI-Greedy, a principled algorithmic framework for addressing this problem.
In particular, we model different fidelities using additive Gaussian processes
based on shared latent structures with the target function. Then we use
cost-sensitive mutual information gain for efficient Bayesian global
optimization. We propose a simple notion of regret which incorporates the cost
of different fidelities, and prove that MF-MI-Greedy achieves low regret. We
demonstrate the strong empirical performance of our algorithm on both synthetic
and real-world datasets.

本文研究了多个输出之间具有复杂结构依赖关系的多认真贝叶斯优化，并提出了 MF-MI-Greedy，一种解决此问题的原则算法框架。