Efficient Full-Matrix Adaptive Regularization
This work addresses the computational bottleneck of full-matrix preconditioning for researchers and practitioners in machine learning, offering an incremental improvement over existing adaptive regularization methods.
The paper tackles the problem of making full-matrix adaptive regularization practical for large-scale machine learning by introducing GGT, an algorithm that efficiently computes the inverse square root of a low-rank matrix, resulting in improved iteration-wise convergence rates in synthetic tasks and deep learning benchmarks.
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 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.