article · 2023

Convex and Nonconvex Sublinear Regression with Application to Data-driven Learning of Reach Sets

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Abstract

We consider estimating a compact set from finite data by approximating the support function of that set via sublinear regression. Support functions uniquely characterize a compact set up to closure of convexification, and are sub-linear (convex as well as positive homogeneous of degree one). Conversely, any sublinear function is the support function of a compact set. We leverage this property to transcribe the task of learning a compact set to that of learning its support function. We propose two algorithms to perform the sublinear regression, one via convex and another via nonconvex programming. The convex programming approach involves solving a quadratic program (QP). The nonconvex programming approach involves training a input sublinear neural network. We illustrate the proposed methods via numerical examples on learning the reach sets of controlled dynamics subject to set-valued input uncertainties from trajectory data.

Cite this paper

APA 7

Haddad, S., & Halder, A. (2023). Convex and Nonconvex Sublinear Regression with Application to Data-driven Learning of Reach Sets. https://doi.org/10.23919/acc55779.2023.10156204

MLA 9

Haddad, Shadi, and Abhishek Halder. “Convex and Nonconvex Sublinear Regression with Application to Data-driven Learning of Reach Sets.” 2023, pp. 4581–86, https://doi.org/10.23919/acc55779.2023.10156204.

Chicago

Haddad, Shadi, and Abhishek Halder. 2023. “Convex and Nonconvex Sublinear Regression with Application to Data-driven Learning of Reach Sets.” https://doi.org/10.23919/acc55779.2023.10156204.

Harvard

Haddad, S. and Halder, A. (2023) ‘Convex and Nonconvex Sublinear Regression with Application to Data-driven Learning of Reach Sets’. Available at: https://doi.org/10.23919/acc55779.2023.10156204.

BibTeX

@article{haddad2023convex,
  title = {{Convex and Nonconvex Sublinear Regression with Application to Data-driven Learning of Reach Sets}},
  author = {Haddad, Shadi and Halder, Abhishek},
  pages = {4581--4586},
  year = {2023},
  doi = {10.23919/acc55779.2023.10156204}
}

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