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910. Inexact Restoration trust-region algorithm with random models for unconstrained noisy optimization

Invited abstract in session TD-32: Algorithms for machine learning and inverse problems: optimisation for neural networks, stream Advances in large scale nonlinear optimization.

Tuesday, 14:30-16:00
Room: 41 (building: 303A)

Authors (first author is the speaker)

1. Simone Rebegoldi
Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università di Modena e Reggio Emilia
2. Benedetta Morini
Dipartimento di Ingegneria Industriale, Universita di Firenze

Abstract

We consider unconstrained smooth optimization problems where the evaluation of both the objective function and its gradient is subject to errors. Particularly, we assume that the function and gradient estimates are random and sufficient accuracy in the estimates can be guaranteed with sufficiently high probability. Following the popular Inexact Restoration framework, we reformulate the original problem as a constrained problem, where the constraint h(y)=0 represents the ideal case in which the function and the gradient are evaluated exactly, being y the noise level and h a non-negative function whose value is related to the accuracy that the estimates can achieve in probability. We show that our problem setting is viable for well-known optimization problems and then design a new trust-region algorithm that employs first-order random models. We analyze the properties of the algorithm and provide the expected number of iterations required to reach an approximate first-order optimality point. We also validate our proposed algorithm on a collection of least-squares problems, showing that it achieves comparable or lower noiseless values on average with respect to a state-of-the-art competitor.

Keywords

Status: accepted

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