Shampoo: Preconditioned Stochastic Tensor Optimization
This addresses the computational bottleneck in optimization for machine learning practitioners, offering a faster-converging method with manageable runtime, though it is an incremental improvement over existing preconditioning techniques.
The paper tackles the problem of large matrix storage and manipulation in preconditioned gradient methods for stochastic optimization over tensor spaces by introducing Shampoo, a structure-aware preconditioning algorithm that uses dimension-specific matrices, and shows it converges faster than common optimizers like SGD, AdaGrad, and Adam in experiments with deep learning models.
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.