论文标题
凸面和非convex sublinear回归，并应用于数据驱动的覆盖范围学习
Convex and Nonconvex Sublinear Regression with Application to Data-driven Learning of Reach Sets
论文作者
论文摘要
我们考虑通过近似sublinear回归估算该集合的支持函数来估算有限数据集的紧凑型集合。支持函数独特地表征了一个紧凑的凸封，并且是sublinear的（凸面和一学位的阳性均匀）。相反，任何sublinear函数都是紧凑型集的支持功能。我们利用此属性来抄录学习紧凑的设置为学习其支持功能的任务。我们提出了两种算法来执行sublinear回归，一种通过凸，另一种通过非凸编程进行。凸编程方法涉及解决二次程序（QP）。 NonConvex编程方法涉及培训输入均方根神经网络。我们通过数值示例来说明所提出的方法，以了解受轨迹数据的设置值输入不确定性的控制动力学的覆盖范围集。
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 sublinear (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.
