In this work we present an "out-of-the-box" application of Machine Learning (ML) optimizers for an industrial optimization problem. We introduce a piecewise polynomial model (spline) for fitting of $\mathcal{C}^k$-continuos functions, which can be deployed in a cam approximation setting. We then use the gradient descent optimization context provided by the machine learning framework TensorFlow to optimize the model parameters with respect to approximation quality and $\mathcal{C}^k$-continuity and evaluate available optimizers. Our experiments show that the problem solution is feasible using TensorFlow gradient tapes and that AMSGrad and SGD show the best results among available TensorFlow optimizers. Furthermore, we introduce a novel regularization approach to improve SGD convergence. Although experiments show that remaining discontinuities after optimization are small, we can eliminate these errors using a presented algorithm which has impact only on affected derivatives in the local spline segment.

翻译：本文提出了一种将机器学习优化器直接应用于工业优化问题的“开箱即用”方案。我们引入了一种分段多项式模型（样条），用于拟合具有$\mathcal{C}^k$连续性的函数，可部署在凸轮逼近场景中。随后，利用机器学习框架TensorFlow提供的梯度下降优化环境，基于逼近质量与$\mathcal{C}^k$连续性对模型参数进行优化，并对现有优化器进行了评估。实验表明，借助TensorFlow梯度带求解该问题具有可行性，且AMSGrad与SGD在现有TensorFlow优化器中表现最佳。此外，我们提出了一种新颖的正则化方法以改善SGD的收敛性。尽管实验显示优化后残留的不连续性较小，但通过所提算法可消除这些误差——该算法仅对局部样条段中受影响的导数产生作用。