Gradient Descent: The Ultimate Optimizer

TL;DR

This paper introduces an automatic method to compute hypergradients via a modification of backpropagation, enabling efficient hyperparameter optimization for various optimizers and reducing sensitivity to initial hyperparameter choices.

Contribution

It presents a simple, elegant approach to automatically compute hypergradients, allowing recursive hyperparameter optimization and broad applicability to different optimizers.

Findings

Validated on MLPs, CNNs, and RNNs

Reduces sensitivity to initial hyperparameters

Provides an accessible PyTorch implementation

Abstract

Working with any gradient-based machine learning algorithm involves the tedious task of tuning the optimizer's hyperparameters, such as its step size. Recent work has shown how the step size can itself be optimized alongside the model parameters by manually deriving expressions for "hypergradients" ahead of time. We show how to automatically compute hypergradients with a simple and elegant modification to backpropagation. This allows us to easily apply the method to other optimizers and hyperparameters (e.g. momentum coefficients). We can even recursively apply the method to its own hyper-hyperparameters, and so on ad infinitum. As these towers of optimizers grow taller, they become less sensitive to the initial choice of hyperparameters. We present experiments validating this for MLPs, CNNs, and RNNs. Finally, we provide a simple PyTorch implementation of this algorithm (see people.csail.mit.edu/kach/gradient-descent-the-ultimate-optimizer).