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Moriconi R, Deisenroth M, Karri S, 2020, High-dimensional Bayesian optimization usinglow-dimensional feature spaces, Machine Learning, Vol: 109, Pages: 1925-1943, ISSN: 0885-6125
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.
Karri SSK, Bach F, Pock T, 2019, Fast decomposable submodular function minimization using constrained total variation, Neural Information Processing Systems, 2019, Publisher: Neural Information Processing Systems Foundation, Inc.
We consider the problem of minimizing the sum of submodular set functions as-suming minimization oracles of each summand function. Most existing approachesreformulate the problem as the convex minimization of the sum of the correspond-ing Lovász extensions and the squared Euclidean norm, leading to algorithmsrequiring total variation oracles of the summand functions; without further assump-tions, these more complex oracles require many calls to the simpler minimizationoracles often available in practice. In this paper, we consider a modified convexproblem requiring a constrained version of the total variation oracles that can besolved with significantly fewer calls to the simple minimization oracles. We supportour claims by showing results on graph cuts for 2D and 3D graphs.
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