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In this paper it is shown that adaptive importance sampling algorithmsconverge at exponential rate for Markov chain expectation problems that admit acombination of a filtered estimator and a Markov zero-variance measure. Itextends a chain of results---special purpose proofs were already known forseveral cases (Kollman et al, Baggerly et al, Desai). A recent paper (Awad etal) provides a complete description of the class of combinations of Markovprocess expectations of path functionals and filtered estimators that admitzero-variance importance measures that retain the Markov property. In a way,this is the maximal class for which adaptive importance sampling algorithmsmight exhibit exponential convergence. The main purpose of this paper is toprove that this is the case: for (most of) those combinations the naturaladaptive importance sampling algorithm converges at exponential rate. Inaddition, the applicability of general Markov chain theory for this purpose isdiscussed through the analysis of a counterexample presented in (Desai andGlynn).

Exponential convergence of adaptive importance sampling estimators for Markov chain expectations