A stochastic first-order trust-region method with inexact restoration for finite-sum minimization

TL;DR

This paper introduces a novel stochastic trust-region method with inexact evaluations for finite-sum minimization, combining inexact restoration and random models to improve efficiency and reduce hyper-parameter tuning.

Contribution

It presents a new stochastic trust-region algorithm that enhances feasibility and optimality in a modular way, with less stringent accuracy requirements and proven iteration complexity.

Findings

Performs well on nonconvex binary classification and regression problems

Reduces the need for hyper-parameter tuning

Achieves efficient convergence with less strict accuracy requirements

Abstract

We propose a stochastic first-order trust-region method with inexact function and gradient evaluations for solving finite-sum minimization problems. Using a suitable reformulation of the given problem, our method combines the inexact restoration approach for constrained optimization with the trust-region procedure and random models. Differently from other recent stochastic trust-region schemes, our proposed algorithm improves feasibility and optimality in a modular way. We provide the expected number of iterations for reaching a near-stationary point by imposing some probability accuracy requirements on random functions and gradients which are, in general, less stringent than the corresponding ones in literature. We validate the proposed algorithm on some nonconvex optimization problems arising in binary classification and regression, showing that it performs well in terms of cost and accuracy, and allows to reduce the burdensome tuning of the hyper-parameters involved.