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.

翻译：本文调查了一类称为线性互补系统(LCS)的计件动物动态系统的学习或系统识别情况。我们建议了一种基于违规的损失,以便能够在不事先了解混合模式界限的情况下,使用梯度方法,有效学习LCS参数化。拟议的基于违规的损失既包括动态预测损失,也包括新的互补性----违约损失。我们显示了通过这种损失表述方法取得的若干特性,包括其差异性、一等和二等衍生物的有效计算及其与传统预测损失的关系,后者严格执行互补性。我们采用这种基于违规的损失配方,以数万种(潜在硬性)混合模式学习LCS参数化。结果表明,最先进的识别计件动物动态的能力,超越了必须通过非线性线性互补问题加以区别的实用方法。