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Efficient Full-Matrix Adaptive Regularization

Naman Agarwal · Brian Bullins · Xinyi Chen · Elad Hazan · Karan Singh · Cyril Zhang · Yi Zhang

Pacific Ballroom #209

Keywords: [ Optimization ] [ Online Learning ] [ Non-convex Optimization ] [ Large Scale Learning and Big Data ]


Adaptive regularization methods pre-multiply a descent direction by a preconditioning matrix. Due to the large number of parameters of machine learning problems, full-matrix preconditioning methods are prohibitively expensive. We show how to modify full-matrix adaptive regularization in order to make it practical and effective. We also provide a novel theoretical analysis for adaptive regularization in {\em non-convex} optimization settings. The core of our algorithm, termed GGT, consists of the efficient computation of the inverse square root of a low-rank matrix. Our preliminary experiments show improved iteration-wise convergence rates across synthetic tasks and standard deep learning benchmarks, and that the more carefully-preconditioned steps sometimes lead to a better solution.

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