Inexact Restoration via random models for unconstrained noisy optimization

Abstract: 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.