We present two sampled quasi-Newton methods: sampled LBFGS and sampled LSR1. Contrary to the classical variants of these methods that sequentially build (inverse) Hessian approximations as the optimization progresses, our proposed methods sample points randomly around the current iterate to produce these approximations. As a result, the approximations constructed make use of more reliable (recent and local) information, and do not depend on past information that could be significantly stale. Our proposed algorithms are efficient in terms of accessed data points (epochs) and have enough concurrency to take advantage of distributed computing environments. We provide convergence guarantees for our proposed methods. Numerical tests on a toy classification problem and on popular benchmarking neural network training tasks reveal that the methods outperform their classical variants and are competitive with first-order methods such as ADAM.
Lehigh University, January 2019