Convergence of adaptive sampling schemes

Overview & Synopsis

In the design of efficient simulation algorithms, one is often beset with a poor choice of proposal distributions. Although the performances of a given kernel can clarify how adequate it is for the problem at hand, a permanent on-line modification of kernels causes concerns about the validity of the resulting algorithm. While the issue is quite complex and most often intractable for MCMC algorithms, the equivalent version for importance sampling algorithms can be validated quite precisely. We derive sufficient convergence conditions for a wide class of population Monte Carlo algorithms and show that Rao-Blackwellized versions asymptotically achieve an optimum in terms of a Kullback divergence criterion, while more rudimentary versions simply do not benefit from repeated updating.