  We present variational inference with sequential sample-average approximation
(VISA), a method for approximate inference in computationally intensive models,
such as those based on numerical simulations. VISA extends importance-weighted
forward-KL variational inference by employing a sequence of sample-average
approximations, which are considered valid inside a trust region. This makes it
possible to reuse model evaluations across multiple gradient steps, thereby
reducing computational cost. We perform experiments on high-dimensional
Gaussians, Lotka-Volterra dynamics, and a Pickover attractor, which demonstrate
that VISA can achieve comparable approximation accuracy to standard
importance-weighted forward-KL variational inference with computational savings
of a factor two or more for conservatively chosen learning rates.
