A General Framework for Multi-fidelity Bayesian Optimization with Gaussian Processes
This addresses the challenge of efficient information gathering in multi-fidelity settings, such as robotics optimization, with a principled approach that improves over existing methods lacking theoretical guarantees.
The paper tackles the problem of optimizing an unknown function using multiple information sources with different costs, such as simulations and real tests, by proposing MF-MI-Greedy, a framework that achieves low regret and demonstrates strong empirical performance on synthetic and real-world datasets.
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.