  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.
