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Published 2010 | Published
Book Section - Chapter Open

Practical Large-Scale Optimization for Max-Norm Regularization


The max-norm was proposed as a convex matrix regularizer in [1] and was shown to be empirically superior to the trace-norm for collaborative filtering problems. Although the max-norm can be computed in polynomial time, there are currently no practical algorithms for solving large-scale optimization problems that incorporate the max-norm. The present work uses a factorization technique of Burer and Monteiro [2] to devise scalable first-order algorithms for convex programs involving the max-norm. These algorithms are applied to solve huge collaborative filtering, graph cut, and clustering problems. Empirically, the new methods outperform mature techniques from all three areas.

Additional Information

©2010 Neural Information Processing Systems. RS supported by NSERC, Shell, and NTT Communication Sciences Laboratory. JAT supported by ONR award N00014-08-1-0883, DARPA award N66001-08-1-2065, and AFOSR award FA9550-09-1-0643. JL thanks TTI Chicago for hosting him while this work was completed.

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August 19, 2023
August 19, 2023