wanxinjin / Learning-LCS

A new learning formulation/method to learn/identify a piecewise linear system, also named as linear complementarity system.

Learning Linear Complementarity Systems

The code is an implementation of the paper Learning Linear Complementarity Systems, coauthored by Wanxin Jin, Alp Aydinoglu, Mathew Halm, and Michael Posa. We have developed a new learning formulation to learn a linear complementarity system (LCS), which consists of a linear dynamics model and complementarity constraint.

Overview

Folder lcs is a python package, which includes

• lcs_learning.py, which packs different utility classes/functions necessary for learning and testing a LCS, particularly including a class LCS_VN for learning a LCS by the proposed violation-based method and a class LCS_PN for learning a LCS by the prediction-based method. For technical details of those two different learning techniques, please refer to our paper.

• optim.py is an implementation of different gradient-based techniques.

Folder evaluations contains different evaluations of the proposed violation-based learning method (LCS_VN) in comparison with the prediction-based method (LCS_PN).

RUN: the quick way to start the code is to run each script in the evaluations folder. All notations/variable used in the code follow the paper or conventions.

Dependency

• CasADi: for solving QP and autodiff. (>= 3.5.1. Info: https://web.casadi.org/), be sure to install qpoases plugin.
• Numpy: for matrix computation. (>= 1.18.1. Info: https://numpy.org/)

Citation

If you find this project/paper helpful in your research, please consider citing our paper.

@misc{jin2021learning,
      title={Learning Linear Complementarity Systems}, 
      author={Wanxin Jin and Alp Aydinoglu and Mathew Halm and Michael Posa},
      year={2021},
      eprint={2112.13284},
      archivePrefix={arXiv},
      primaryClass={cs.LG}
}