Multi-Domain Adaptive Learning Based on Feasibility Splitting and Adaptive Projected Subgradient Method

Abstract

We propose the multi-domain adaptive learning that enables us to find a point meeting possibly time-varying specifications simultaneously in multiple domains, e.g. space, time, frequency, etc. The novel concept is based on the idea of feasibility splitting—dealing with feasibility in each individual domain. We show that the adaptive projected subgradient method (Yamada, 2003) realizes the multi-domain adaptive learning by employing (i) a projected gradient operator with respect to a 'fixed' proximity function reflecting the time-invariant specifications and (ii) a subgradient projection with respect to 'time-varying' objective functions reflecting the time-varying specifications. The resulting algorithm is suitable for real-time implementation, because it requires no more than metric projections onto closed convex sets each of which accommodates the specification in each domain. A convergence analysis and numerical examples are presented.