Affinely constrained online learning and its application to beamforming

This paper presents a novel method for incorporating a-priori affine constraints in online kernel-based learning tasks. The proposed technique elaborates the generic tool of projections to form a sequence of estimates in reproducing kernel Hilbert spaces (RKHS). The method guarantees that the whole sequence of estimates lies in the given affine constraint set. To validate the algorithm, a beamforming task is considered. The numerical results show that the proposed frame provides with solutions in cases where the classical linear approach collapses, and forms proper beam-patterns as opposed to a recent unconstrained kernel-based regression method.