  Approximating a probability density in a tractable manner is a central task
in Bayesian statistics. Variational Inference (VI) is a popular technique that
achieves tractability by choosing a relatively simple variational family.
Borrowing ideas from the classic boosting framework, recent approaches attempt
to \emph{boost} VI by replacing the selection of a single density with a
greedily constructed mixture of densities. In order to guarantee convergence,
previous works impose stringent assumptions that require significant effort for
practitioners. Specifically, they require a custom implementation of the greedy
step (called the LMO) for every probabilistic model with respect to an
unnatural variational family of truncated distributions. Our work fixes these
issues with novel theoretical and algorithmic insights. On the theoretical
side, we show that boosting VI satisfies a relaxed smoothness assumption which
is sufficient for the convergence of the functional Frank-Wolfe (FW) algorithm.
Furthermore, we rephrase the LMO problem and propose to maximize the Residual
ELBO (RELBO) which replaces the standard ELBO optimization in VI. These
theoretical enhancements allow for black box implementation of the boosting
subroutine. Finally, we present a stopping criterion drawn from the duality gap
in the classic FW analyses and exhaustive experiments to illustrate the
usefulness of our theoretical and algorithmic contributions.
