Gradient Methods with Online Scaling Part II. Practical Aspects
This work addresses optimization efficiency for machine learning practitioners by providing a practical, memory-efficient alternative to quasi-Newton methods, though it is incremental as it builds on prior theoretical foundations.
The paper tackles practical implementation of online scaled gradient methods (OSGM) by designing new adaptive first-order methods, resulting in OSGM-Best, which matches quasi-Newton performance with less memory and cheaper iterations.
Part I of this work [Gao25] establishes online scaled gradient methods (OSGM), a framework that utilizes online convex optimization to adapt stepsizes in gradient methods. This paper focuses on the practical aspects of OSGM. We leverage the OSGM framework to design new adaptive first-order methods and provide insights into their empirical behavior. The resulting method, OSGM-Best, matches the performance of quasi-Newton variants while requiring less memory and cheaper iterations. We also extend OSGM to nonconvex optimization and outline directions that connect OSGM to existing branches of optimization theory and practice.