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Global convergence rate analysis of unconstrained optimization methods based on probabilistic models

Coralia Cartis(coralia.cartis***at***maths.ox.ac.uk )
Katya Scheinberg(katyascheinberg***at***gmail.com)

Abstract: We present global convergence rates for a line-search method which is based on random first-order models and directions whose quality is ensured only with certain probability. We show that in terms of the order of the accuracy, the evaluation complexity of such a method is the same as its counterparts that use deterministic accurate models; the use of probabilistic models only increases the complexity by a constant, which depends on the probability of the models being good. We particularize and improve these results in the convex and strongly convex case. We also analyse a probabilistic cubic regularization variant that allows approximate probabilistic second-order models and show improved complexity bounds compared to probabilistic first-order methods; again, as a function of the accuracy, the probabilistic cubic regularization bounds are of the same (optimal) order as for the deterministic case.

Keywords: line-search methods, cubic regularization methods, random models, global convergence analysis

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Citation: Lehigh University, May 2015

Download: [PDF]

Entry Submitted: 05/22/2015
Entry Accepted: 05/22/2015
Entry Last Modified: 05/22/2015

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