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

Masahiro YUKAWA  Konstantinos SLAVAKIS  Isao YAMADA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E93-A   No.2   pp.456-466
Publication Date: 2010/02/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E93.A.456
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Digital Signal Processing
Keyword: 
adaptive algorithm,  convex projection,  projected gradient method,  convex feasibility problem,  

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Summary: 
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.