Bayesian optimization (BO) methods often rely on the assumption that the objective function is well-behaved, but in practice the objective functions are seldom well-behaved even if noise-free observations can be collected. We propose to address the issue by focusing on the well-behaved structure informative for search while ignoring detrimental structure that is challenging to model data efficiently. We use a noise distribution to absorb the challenging details by treating them as irreducible uncertainty. In particular we use a latent Gaussian process as the surrogate model, in which a latent variable is introduced to the input of a Gaussian process and serves as a noise variable. It allows the noise distribution to be non-stationary and non-Gaussian. With experiments on a range of BO benchmarks, we show that our method significantly outperform existing methods. Keywords: robust surrogate models, Bayesian Optimization, nonsmooth objective functions, Latent Gaussian Processes
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