Bayesian Optimization with Unknown Constraints

Gelbart, M. A., Snoek, J., & Adams, R. P. (2014). Bayesian Optimization with Unknown Constraints. Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence (UAI).
Recent work on Bayesian optimization has shown its effectiveness in global optimization of difficult black-box objective functions. Many real-world optimization problems of interest also have constraints which are unknown a priori. In this paper, we study Bayesian optimization for constrained problems in the general case that noise may be present in the constraint functions, and the objective and constraints may be evaluated independently. We provide motivating practical examples, and present a general frame- work to solve such problems. We demonstrate the effectiveness of our approach on optimizing the performance of online latent Dirichlet allocation subject to topic sparsity constraints, tun- ing a neural network given test-time memory constraints, and optimizing Hamiltonian Monte Carlo to achieve maximal effectiveness in a fixed time, subject to passing standard convergence diagnostics.
  year = {2014},
  author = {Gelbart, Michael A. and Snoek, Jasper and Adams, Ryan P.},
  title = {Bayesian Optimization with Unknown Constraints},
  booktitle = {Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence (UAI)},
  keywords = {Bayesian optimization, UAI},
  note = {arXiv:1403.5607 [stat.ML]}