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We propose a general technique for improving alternating optimization (AO) ofnonconvex functions. Starting from the solution given by AO, we conduct anothersequence of searches over subspaces that are both meaningful to theoptimization problem at hand and different from those used by AO. Todemonstrate the utility of our approach, we apply it to the matrixfactorization (MF) algorithm for recommender systems and the coordinate descentalgorithm for penalized regression (PR), and show meaningful improvements usingboth real-world (for MF) and simulated (for PR) data sets. Moreover, wedemonstrate for MF that, by constructing search spaces customized to the givendata set, we can significantly increase the convergence rate of our technique.

Expanded Alternating Optimization of Nonconvex Functions with Applications to Matrix Factorization and Penalized Regression