We present a universally consistent learning rule whose expected error is monotone non-increasing with the sample size under every data distribution. The question of existence of such rules was brought up in 1996 by Devroye, Gy\"orfi and Lugosi (who called them "smart"). Our rule is fully deterministic, a data-dependent partitioning rule constructed in an arbitrary domain (a standard Borel space) using a cyclic order. The central idea is to only partition at each step those cyclic intervals that exhibit a sufficient empirical diversity of labels, thus avoiding a region where the error function is convex.

翻译：我们提出了一个普遍一致的学习规则,其预期的错误是单一的,不会随着每个数据分布的样本大小而增加。 1996年,Devroye、Gy\'orfi和Lugosi(他们称它们为“聪明 ” ) 提出了这种规则的存在问题。 我们的规则是完全确定性的,这是在任意领域(标准波雷尔空间)用一个周期顺序构建的依赖于数据的分割规则。 中心思想是,在每一步只分出那些显示足够不同标签的经验间隔,从而避免一个错误函数为曲线的区域。