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# Structured Variationally Auto-encoded Optimization

*Proceedings of the 35th International Conference on Machine Learning*, PMLR 80:3273-3281, 2018.

#### Abstract

We tackle the problem of optimizing a black-box objective function
defined over a highly-structured input space. This problem is
ubiquitous in science and engineering. In machine learning,
inferring the structure of a neural network or the Automatic
Statistician (AS), where the optimal kernel combination for a
Gaussian process is selected, are two important examples. We use the
\as as a case study to describe our approach, that can be easily
generalized to other domains. We propose an Structure Generating
Variational Auto-encoder (SG-VAE) to embed the original space of
kernel combinations into some low-dimensional continuous manifold
where Bayesian optimization (BO) ideas are used. This is possible
when structural knowledge of the problem is available, which can be
given via a simulator or any other form of generating potentially
good solutions. The right exploration-exploitation balance is
imposed by propagating into the search the uncertainty of the latent
space of the SG-VAE, that is computed using variational
inference. The key aspect of our approach is that the SG-VAE can be
used to bias the search towards relevant regions, making it suitable
for transfer learning tasks. Several experiments in various
application domains are used to illustrate the utility and
generality of the approach described in this work.