Understanding and correcting pathologies in the training of learned optimizers

TL;DR

This paper introduces a new training scheme for learned optimizers that overcomes key difficulties, enabling them to outperform traditional optimizers in specific tasks in terms of speed and test loss.

Contribution

A novel training method for learned optimizers that balances unbiased gradient estimators, improving their training stability and effectiveness.

Findings

Learned optimizers trained with our method outperform tuned first-order methods in wall-clock time.

Our approach reduces training pathologies like biased gradients and exploding norms.

The learned optimizers achieve better test loss on convolutional network training tasks.

Abstract

Deep learning has shown that learned functions can dramatically outperform hand-designed functions on perceptual tasks. Analogously, this suggests that learned optimizers may similarly outperform current hand-designed optimizers, especially for specific problems. However, learned optimizers are notoriously difficult to train and have yet to demonstrate wall-clock speedups over hand-designed optimizers, and thus are rarely used in practice. Typically, learned optimizers are trained by truncated backpropagation through an unrolled optimization process resulting in gradients that are either strongly biased (for short truncations) or have exploding norm (for long truncations). In this work we propose a training scheme which overcomes both of these difficulties, by dynamically weighting two unbiased gradient estimators for a variational loss on optimizer performance, allowing us to train neural networks to perform optimization of a specific task faster than tuned first-order methods. We demonstrate these results on problems where our learned optimizer trains convolutional networks faster in wall-clock time compared to tuned first-order methods and with an improvement in test loss.