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

Coralia Cartis; Katya Scheinberg

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arXiv · 1505.06070

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

Coralia Cartis·Katya Scheinberg

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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 analyze 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.

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BibTeX RIS

Coralia Cartis, Katya Scheinberg. 2015-05-22. Global convergence rate analysis of unconstrained optimization methods based on probabilistic models. https://arxiv.org/abs/1505.06070

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