FOSI: Hybrid First and Second Order Optimization
Authors: Hadar Sivan,Moshe Gabel,Assaf Schuster
Presentation: ICLR 2024,Poster

Abstract: Popular machine learning approaches forgo second-order information due to the difficulty of computing curvature in high dimensions.
We present FOSI, a novel meta-algorithm that improves the performance of any base first-order optimizer by efficiently incorporating second-order information during the optimization process.
In each iteration, FOSI implicitly splits the function into two quadratic functions defined on orthogonal subspaces, then uses a second-order method to minimize the first, and the base optimizer to minimize the other.
We formally analyze FOSI's convergence and the conditions under which it improves a base optimizer.
Our empirical evaluation 
demonstrates that FOSI improves the convergence rate and optimization time of first-order methods such as Heavy-Ball and Adam, and outperforms second-order methods (K-FAC and L-BFGS).