FOSI: Hybrid First and Second Order Optimization
This work addresses optimization efficiency for machine learning practitioners, offering a hybrid approach that is incremental but provides measurable gains.
The paper tackles the challenge of incorporating second-order information in high-dimensional optimization by introducing FOSI, a meta-algorithm that improves first-order optimizers like Heavy-Ball and Adam, resulting in faster convergence rates and optimization times compared to methods such as K-FAC and L-BFGS.
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).