Adaptive learning in a world of projections

This article presents a general tool for convexly constrained parameter/function estimation both for classification and regression tasks, in a time-adaptive setting and in (infinite dimensional) Reproducing Kernel Hilbert Spaces (RKHS). The mathematical framework is that of the set theoretic estimation formulation and the classical projections onto convex sets (POCS) theory. However, in contrast to the classical POCS methodology, which assumes a finite number of convex sets, our method builds upon our recent extension of the theory, which considers an infinite number of convex sets. Such a context is necessary to cope with the adaptive setting rationale, where data arrive sequentially.