Learning Linear Complementarity Systems

TL;DR

This paper introduces a violation-based loss function for efficiently learning linear complementarity systems (LCSs) without prior mode boundary knowledge, enabling accurate system identification with gradient-based methods.

Contribution

It proposes a novel violation-based loss that combines dynamics prediction and complementarity enforcement, improving learning efficiency and accuracy for complex hybrid systems.

Findings

Achieves state-of-the-art identification of piecewise-affine dynamics.

Effectively learns LCSs with thousands of hybrid modes.

Outperforms existing methods that differentiate through non-smooth problems.

Abstract

This paper investigates the learning, or system identification, of a class of piecewise-affine dynamical systems known as linear complementarity systems (LCSs). We propose a violation-based loss which enables efficient learning of the LCS parameterization, without prior knowledge of the hybrid mode boundaries, using gradient-based methods. The proposed violation-based loss incorporates both dynamics prediction loss and a novel complementarity - violation loss. We show several properties attained by this loss formulation, including its differentiability, the efficient computation of first- and second-order derivatives, and its relationship to the traditional prediction loss, which strictly enforces complementarity. We apply this violation-based loss formulation to learn LCSs with tens of thousands of (potentially stiff) hybrid modes. The results demonstrate a state-of-the-art ability to identify piecewise-affine dynamics, outperforming methods which must differentiate through non-smooth linear complementarity problems.