Shampoo: Preconditioned Stochastic Tensor Optimization

Code

• github.com/kazukiosawa/asdfghjkl
  pytorch★ 192
• github.com/kazukiosawa/asdl
  pytorch★ 192
• github.com/Daniil-Selikhanovych/Shampoo_optimizer
  tf★ 0

Abstract

Preconditioned gradient methods are among the most general and powerful tools in optimization. However, preconditioning requires storing and manipulating prohibitively large matrices. We describe and analyze a new structure-aware preconditioning algorithm, called Shampoo, for stochastic optimization over tensor spaces. Shampoo maintains a set of preconditioning matrices, each of which operates on a single dimension, contracting over the remaining dimensions. We establish convergence guarantees in the stochastic convex setting, the proof of which builds upon matrix trace inequalities. Our experiments with state-of-the-art deep learning models show that Shampoo is capable of converging considerably faster than commonly used optimizers. Although it involves a more complex update rule, Shampoo's runtime per step is comparable to that of simple gradient methods such as SGD, AdaGrad, and Adam.

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