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arXiv · 2311.13544

Piecewise Polynomial Regression of Tame Functions via Integer Programming

Gilles Bareilles·Johannes Aspman·Jiri Nemecek·Jakub Marecek
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Abstract

Tame functions are a class of nonsmooth, nonconvex functions, which feature in a wide range of applications: functions encountered in the training of deep neural networks with all common activations, value functions of mixed-integer programs, or wave functions of small molecules. We consider approximating tame functions with piecewise polynomial functions. We bound the quality of approximation of a tame function by a piecewise polynomial function with a given number of segments on any full-dimensional cube. We also present the first mixed-integer programming formulation of piecewise polynomial regression. Together, these can be used to estimate tame functions. We demonstrate promising computational results.

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Gilles Bareilles, Johannes Aspman, Jiri Nemecek, Jakub Marecek. 2023-11-22. Piecewise Polynomial Regression of Tame Functions via Integer Programming. https://arxiv.org/abs/2311.13544

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