A Simple Algorithm for Nuclear Norm Regularized Problems
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Abstract
Optimization problems with a nuclear norm regularization, such as e.g. low norm matrix factorizations, have seen many applications recently. We propose a new approximation algorithm building upon the recent sparse approximate SDP solver of (Hazan, 2008). The experimental efficiency of our method is demonstrated on large matrix completion problems such as the Netflix dataset. The algorithm comes with strong convergence guarantees, and can be interpreted as a first theoretically justified variant of Simon-Funk-type SVD heuristics. The method is free of tuning parameters, and very easy to parallelize.
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