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

A universally consistent learning rule with a universally monotone error