High-dimensional Bayesian optimization using low-dimensional feature spaces

Abstract

Bayesian optimization (BO) is a powerful approach for seeking the global optimum of expensive black-box functions and has proven successful for fine tuning hyper-parameters of machine learning models. However, BO is practically limited to optimizing 10–20 parameters. To scale BO to high dimensions, we usually make structural assumptions on the decomposition of the objective and/or exploit the intrinsic lower dimensionality of the problem, e.g. by using linear projections. We could achieve a higher compression rate with nonlinear projections, but learning these nonlinear embeddings typically requires much data. This contradicts the BO objective of a relatively small evaluation budget. To address this challenge, we propose to learn a low-dimensional feature space jointly with (a) the response surface and (b) a reconstruction mapping. Our approach allows for optimization of BO’s acquisition function in the lower-dimensional subspace, which significantly simplifies the optimization problem. We reconstruct the original parameter space from the lower-dimensional subspace for evaluating the black-box function. For meaningful exploration, we solve a constrained optimization problem.

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“…Furthermore, in the GPSG approach, additional or alternative level 0 can be easily incorporated. Possible extensions to our approach include combination with methods to adaptively reduce the input space for constrained optimization problems ( 42 ), or other emulators may be chosen depending on the application. For example, homoscedastic GPs, which are faster than the heteroscedastic approach presented here, may be sufficient for many applications (but not for our IBM in which heteroscedastic was required due to the stochastic nature of the model).…”