Almost sure and Lq-convergence of the re-initialized BMP scheme

Gerencsér, László and Mátyás, Zalán (2007) Almost sure and Lq-convergence of the re-initialized BMP scheme. In: CDC 2007. Proceedings of the 46th IEEE conference on decision and control. New Orleans, 2007..

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Abstract

We consider stochastic approximation algorithms with Markovian dynamics introduced by Benveniste, Métivier and Priouret in their 1990 book. A major deficiency of the BMP theory is that it guarantees convergence only with probability strictly less than 1. This deficiency will be overcome by incorporating a resetting mechanism for the parameter with a fairly arbitrary truncation domain. At the same time the state is also reset. The algorithm is shown to converge to the assumed unique stationary point of the associated ODE with probability 1. The result is complementary to a similar result by Delyon, which uses a different modification and stronger assumptions. An outline to the basic technical aspects of the BMP theory will be also given.

Item Type: Conference or Workshop Item (Paper)
Uncontrolled Keywords: stochastic systems; Markovian dynamics; recursive estimation; resetting.
Subjects: Q Science > QA Mathematics and Computer Science > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány
Depositing User: Eszter Nagy
Date Deposited: 11 Dec 2012 15:29
Last Modified: 11 Dec 2012 15:29
URI: http://eprints.sztaki.hu/id/eprint/4990

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