Training Deep Learning Models with Norm-Constrained LMOs

TL;DR

This paper introduces a novel stochastic optimization algorithm leveraging the linear minimization oracle over norm-balls, which adapts to problem geometry, applies to unconstrained problems, and accelerates deep model training.

Contribution

It presents a new family of algorithms using LMOs for adaptive optimization, unifies existing methods, and demonstrates practical speedups in deep learning training without relying on Adam.

Findings

Significant speedups in nanoGPT training with the Scion algorithm

Memory-efficient optimization requiring only one set of weights and gradients

Transferability of hyperparameters across different model sizes

Abstract

In this work, we study optimization methods that leverage the linear minimization oracle (LMO) over a norm-ball. We propose a new stochastic family of algorithms that uses the LMO to adapt to the geometry of the problem and, perhaps surprisingly, show that they can be applied to unconstrained problems. The resulting update rule unifies several existing optimization methods under a single framework. Furthermore, we propose an explicit choice of norm for deep architectures, which, as a side benefit, leads to the transferability of hyperparameters across model sizes. Experimentally, we demonstrate significant speedups on nanoGPT training using our algorithm, Scion, without any reliance on Adam. The proposed method is memory-efficient, requiring only one set of model weights and one set of gradients, which can be stored in half-precision. The code is available at https://github.com/LIONS-EPFL/scion .