Abstract
Sequential and Quantum Monte Carlo methods, as well as genetic type search algorithms can be interpreted as a mean field and interacting particle approximations of Feynman-Kac models in distribution spaces. The performance of these population Monte Carlo algorithms is related to the stability properties of nonlinear Feynman-Kac semigroups. In this paper, we analyze these models in terms of Dobrushin ergodic coefficients of the reference Markov transitions and the oscillations of the potential functions. Sufficient conditions for uniform concentration inequalities w.r.t. time are expressed explicitly in terms of these two quantities. Special attention is devoted to the particular case of Boltzmann-Gibbs measures’ sampling. In this context, we design an explicit way of tuning the temperature schedule with the number of Markov Chain Monte Carlo iterations.
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Giraud, F., Del Moral, P. (2013). On the Convergence of Quantum and Sequential Monte Carlo Methods. In: Dick, J., Kuo, F., Peters, G., Sloan, I. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2012. Springer Proceedings in Mathematics & Statistics, vol 65. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41095-6_17
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DOI: https://doi.org/10.1007/978-3-642-41095-6_17
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