Gradient descent with generalized Newton's method

TL;DR

The paper introduces the generalized Newton's method (GeN), a Hessian-informed optimizer that automatically adjusts learning rates for faster convergence without extensive tuning, applicable to various optimizers like SGD and Adam.

Contribution

It presents a new optimizer, GeN, that dynamically selects learning rates, improving convergence speed and ease of implementation across different models and tasks.

Findings

GeN matches state-of-the-art performance on language and vision tasks.

GeN requires minimal additional computation and no extensive tuning.

Experiments demonstrate GeN's effectiveness across GPT and ResNet models.

Abstract

We propose the generalized Newton's method (GeN) -- a Hessian-informed approach that applies to any optimizer such as SGD and Adam, and covers the Newton-Raphson method as a sub-case. Our method automatically and dynamically selects the learning rate that accelerates the convergence, without the intensive tuning of the learning rate scheduler. In practice, our method is easily implementable, since it only requires additional forward passes with almost zero computational overhead (in terms of training time and memory cost), if the overhead is amortized over many iterations. We present extensive experiments on language and vision tasks (e.g. GPT and ResNet) to showcase that GeN optimizers match the state-of-the-art performance, which was achieved with carefully tuned learning rate schedulers.