  Approximate Bayesian Computation (ABC) is a framework for performing
likelihood-free posterior inference for simulation models. Stochastic
Variational inference (SVI) is an appealing alternative to the inefficient
sampling approaches commonly used in ABC. However, SVI is highly sensitive to
the variance of the gradient estimators, and this problem is exacerbated by
approximating the likelihood. We draw upon recent advances in variance
reduction for SV and likelihood-free inference using deterministic simulations
to produce low variance gradient estimators of the variational lower-bound. By
then exploiting automatic differentiation libraries we can avoid nearly all
model-specific derivations. We demonstrate performance on three problems and
compare to existing SVI algorithms. Our results demonstrate the correctness and
efficiency of our algorithm.
