From Learning to Optimize to Learning Optimization Algorithms

TL;DR

This paper introduces a principled approach to designing learned optimization algorithms that generalize beyond their training data by integrating classical optimization principles with learning strategies.

Contribution

It proposes a general design pipeline for learning optimization algorithms based on classical principles, enabling broader applicability and improved performance.

Findings

The learned algorithms outperform traditional methods on various tasks.

A new learning-enhanced BFGS algorithm demonstrates strong adaptability.

Numerical experiments confirm the effectiveness of the proposed principles.

Abstract

Towards designing learned optimization algorithms that are usable beyond their training setting, we identify key principles that classical algorithms obey, but have up to now, not been used for Learning to Optimize (L2O). Following these principles, we provide a general design pipeline, taking into account data, architecture and learning strategy, and thereby enabling a synergy between classical optimization and L2O, resulting in a philosophy of Learning Optimization Algorithms. As a consequence our learned algorithms perform well far beyond problems from the training distribution. We demonstrate the success of these novel principles by designing a new learning-enhanced BFGS algorithm and provide numerical experiments evidencing its adaptation to many settings at test time.