Speeding up Monte Carlo Integration: Control Neighbors for Optimal Convergence
par
Johan Segers(UC Louvain)
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Europe/Paris
Amphi. Schwartz (1R3)
Amphi. Schwartz
1R3
Description
This paper investigates a novel linear integration rule called control neighbors based on nearest neighbor estimates acting as control variates to speed up the convergence rate of the Monte Carlo procedure. The main result is the $O(n^{-1/2} n^{-1/d})$ convergence rate -- where n stands for the number of evaluations of the integrand -- of this estimate for Lipschitz functions, a rate which, in some sense, is optimal. Several numerical experiments validate the complexity bound and highlight the good performance of the proposed estimator.
This is a joint work with Rémi Leluc, François Portier and Aigerim Zhuman.