A Simple Guard for Learned Optimizers

TL;DR

This paper introduces Loss-Guarded L2O, a simpler and more efficient safeguarding method for learned optimizers that guarantees convergence and outperforms previous safeguard techniques in practice.

Contribution

It proposes Loss-Guarded L2O, a novel safeguarding approach that is simpler, computationally cheaper, and provably convergent, improving the robustness and effectiveness of learned optimizers.

Findings

LGL2O converges better than GL2O in experiments.

LGL2O combines strengths of L2O and SGD.

Theoretical proof of convergence for LGL2O.

Abstract

If the trend of learned components eventually outperforming their hand-crafted version continues, learned optimizers will eventually outperform hand-crafted optimizers like SGD or Adam. Even if learned optimizers (L2Os) eventually outpace hand-crafted ones in practice however, they are still not provably convergent and might fail out of distribution. These are the questions addressed here. Currently, learned optimizers frequently outperform generic hand-crafted optimizers (such as gradient descent) at the beginning of learning but they generally plateau after some time while the generic algorithms continue to make progress and often overtake the learned algorithm as Aesop's tortoise which overtakes the hare. L2Os also still have a difficult time generalizing out of distribution. Heaton et al. proposed Safeguarded L2O (GL2O) which can take a learned optimizer and safeguard it with a generic learning algorithm so that by conditionally switching between the two, the resulting algorithm is provably convergent. We propose a new class of Safeguarded L2O, called Loss-Guarded L2O (LGL2O), which is both conceptually simpler and computationally less expensive. The guarding mechanism decides solely based on the expected future loss value of both optimizers. Furthermore, we show theoretical proof of LGL2O's convergence guarantee and empirical results comparing to GL2O and other baselines showing that it combines the best of both L2O and SGD and that in practice converges much better than GL2O.