In this paper, we propose a stochastic optimization method that adaptively controls the sample size used in the computation of gradient approximations. Unlike other variance reduction techniques that either require additional storage or the regular computation of full gradients, the proposed method reduces variance by increasing the sample size as needed. The decision to increase the sample size is governed by an inner product test that ensures that search directions are descent directions with high probability. We show that the inner product test improves upon the well known norm test, and can be used as a basis for an algorithm that is globally convergent on nonconvex functions and enjoys a global linear rate of convergence on strongly convex functions. Numerical experiments on logistic regression problems illustrate the performance of the algorithm.
More recently, in REF , the authors introduced a first order algorithm for unconstrained stochastic convex programs that involves choosing sample size dependents on an inner product test to find a descent direction with high probability.
Adaptive Sampling Strategies for Stochastic Optimization
arXiv: Optimization and Control
Computer Science Mathematics