Adaptive Sampling Strategies for Stochastic Optimization

TL;DR

This paper introduces an adaptive stochastic optimization method that dynamically adjusts sample sizes based on an inner product test, achieving global convergence and efficient variance reduction without full gradient computations.

Contribution

The paper presents a novel adaptive sampling strategy using an inner product test, improving variance control and convergence guarantees over existing methods.

Findings

The method ensures descent directions with high probability.

It achieves global convergence on nonconvex functions.

It attains a linear convergence rate on strongly convex functions.

Abstract

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.