We present an improved algorithm for {\em quasi-properly} learning convex polyhedra in the realizable PAC setting from data with a margin. Our learning algorithm constructs a consistent polyhedron as an intersection of about $t \log t$ halfspaces with constant-size margins in time polynomial in $t$ (where $t$ is the number of halfspaces forming an optimal polyhedron). We also identify distinct generalizations of the notion of margin from hyperplanes to polyhedra and investigate how they relate geometrically; this result may have ramifications beyond the learning setting.

翻译：我们在可实现的 PAC 设置中,根据带有差值的数据,我们提出了一个改进的计算法,用于在可实现的 PAC 设置中学习 convex monhedra 。我们的学习算法构建了一个一致的多面形,将一个大约为$t\log t$半空的交叉点,以美元计时多面间距不变(美元,美元是形成最佳多元面的半空空间的数量 ) 。 我们还确定了从超浮机到多面的差概念的不同概观,并调查它们与几何性的关系;这一结果可能会产生超出学习环境的影响。