  Naive approaches to amortized inference in probabilistic programs with
unbounded loops can produce estimators with infinite variance. This is
particularly true of importance sampling inference in programs that explicitly
include rejection sampling as part of the user-programmed generative procedure.
In this paper we develop a new and efficient amortized importance sampling
estimator. We prove finite variance of our estimator and empirically
demonstrate our method's correctness and efficiency compared to existing
alternatives on generative programs containing rejection sampling loops and
discuss how to implement our method in a generic probabilistic programming
framework.
