Adaptive Overrelaxed Bound Optimization Methods

Ruslan Salakhutdinov and Sam Roweis

We study a class of overrelaxed bound optimization algorithms, and their relationship to standard bound optimizers, such as Expectation-Maximization, Iterative Scaling, CCCP and Non-Negative Matrix Factorization. We provide a theoretical analysis of the convergence properties of these optimizers and identify analytic conditions under which they are expected to outperform the standard versions. Based on this analysis, we propose a novel, simple adaptive overrelaxed scheme for practical optimization and report empirical results on several synthetic and real-world data sets showing that these new adaptive methods exhibit superior performance (in certain cases by several times speedup) compared to their traditional counterparts. Our extensions are simple to implement, apply to a wide variety of algorithms, almost always give a substantial speedup, and do not require any theoretical analysis of the underlying algorithm.

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