  We study the Inexact Restoration framework with random models for minimizing
functions whose evaluation is subject to errors. We propose a constrained
formulation that includes well-known stochastic problems and an algorithm
applicable when the evaluation of both the function and its gradient is random
and a specified accuracy of such evaluations is guaranteed with sufficiently
high probability. The proposed algorithm combines the Inexact Restoration
framework with a trust-region methodology based on random first-order models.
We analyse the properties of the algorithm and provide the expected number of
iterations performed to reach an approximate first-order optimality point.
Numerical experiments show that the proposed algorithm compares well with a
state-of-the-art competitor.
