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FOSI: Hybrid First and Second Order Optimization

Hadar Sivan · Moshe Gabel · Assaf Schuster

Halle B #209
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Wed 8 May 1:45 a.m. PDT — 3:45 a.m. PDT


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).

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