L-SR1: Learned Symmetric-Rank-One Preconditioning

TL;DR

This paper introduces L-SR1, a learned second-order optimizer with a trainable preconditioning unit that improves convergence and generalization in optimization tasks, demonstrated on Monocular Human Mesh Recovery.

Contribution

It presents a novel learned second-order optimizer that integrates a trainable preconditioning unit into the classical SR1 algorithm, enhancing efficiency and applicability.

Findings

Outperforms existing learned optimizers on HMR task

Requires no annotated data or fine-tuning

Offers strong generalization and lightweight design

Abstract

End-to-end deep learning has achieved impressive results but remains limited by its reliance on large labeled datasets, poor generalization to unseen scenarios, and growing computational demands. In contrast, classical optimization methods are data-efficient and lightweight but often suffer from slow convergence. While learned optimizers offer a promising fusion of both worlds, most focus on first-order methods, leaving learned second-order approaches largely unexplored. We propose a novel learned second-order optimizer that introduces a trainable preconditioning unit to enhance the classical Symmetric-Rank-One (SR1) algorithm. This unit generates data-driven vectors used to construct positive semi-definite rank-one matrices, aligned with the secant constraint via a learned projection. Our method is evaluated through analytic experiments and on the real-world task of Monocular Human Mesh Recovery (HMR), where it outperforms existing learned optimization-based approaches. Featuring a lightweight model and requiring no annotated data or fine-tuning, our approach offers strong generalization and is well-suited for integration into broader optimization-based frameworks.