We study the problem of binary classification from the point of view of learning convex polyhedra in Hilbert spaces, to which one can reduce any binary classification problem. The problem of learning convex polyhedra in finite-dimensional spaces is sufficiently well studied in the literature. We generalize this problem to that in a Hilbert space and propose an algorithm for learning a polyhedron which correctly classifies at least $1- \varepsilon$ of the distribution, with a probability of at least $1 - \delta,$ where $\varepsilon$ and $\delta$ are given parameters. Also, as a corollary, we improve some previous bounds for polyhedral classification in finite-dimensional spaces.

翻译：我们从学习Hilbert空间的二次曲线多元赫德拉的角度来看研究二进制分类问题,这样可以减少任何二进制分类问题。在有限维度空间学习二次曲线多元赫德拉的问题在文献中研究得足够周密。我们将此问题推广到Hilbert空间,并提议一种计算法,用于学习至少1美元-毫瓦列普西隆的多元希德龙,该计算法可以正确分类分配至少1美元-毫德罗元,其中提供参数的值为$-瓦列普西隆和$-德尔塔元。此外,作为必然结果,我们改进了某些以往在有限维度空间进行多元分类的界限。</s>