Sequential Experimental Design and Optimization with Structural Assumptions: Additivity and Subspaces

Mutny, Mojmir and Krause, Andreas, Sequential Experimental Design and Optimization with Structural Assumptions: Additivity and Subspaces.”, 2024. (in preparation for JMLR)

Abstract: Experiment design in high-dimensional problems is an important practical problem in many fields of science. Without further structural assumptions, the experiment design algorithms based on reproducing kernel hilbert spaces with classical kernels suffer from curse of dimensionality. In this work we explore additional structural assumptions of additive structure or variability in low dimensional linear subspace. We present the prior works in unified framework and analyze the projection pursuit regression models in the context of experiment design, which strictly generalize additive models. We combine them with potentially non-linear effective dimension via manifold projection pursuit regression model. We contrast to other methods developed and we address practical issues such as acquisition function optimization.

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