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Stochastic Optimization on Continuous Domains With Finite-Time Guarantees by Markov Chain Monte Carlo Methods

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3 Author(s)
Andrea Lecchini-Visintini ; Department of Engineering, University of Leicester, U.K. ; John Lygeros ; Jan M. Maciejowski

We introduce bounds on the finite-time performance of Markov chain Monte Carlo (MCMC) algorithms in solving global stochastic optimization problems defined over continuous domains. It is shown that MCMC algorithms with finite-time guarantees can be developed with a proper choice of the target distribution and by studying their convergence in total variation norm. This work is inspired by the concept of finite-time learning with known accuracy and confidence developed in statistical learning theory.

Published in:

IEEE Transactions on Automatic Control  (Volume:55 ,  Issue: 12 )