The Mathematical Institute, University of Oxford, Eprints Archive

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

Cartis, Coralia and Scheinberg, Katya (2015) Global convergence rate analysis of unconstrained optimization methods based on probabilistic models. Technical Report. Unspecified. (Submitted)

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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.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1887
Deposited By: Helen Taylor
Deposited On:27 May 2015 08:12
Last Modified:29 May 2015 19:35

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