  This paper introduces a variational approximation framework using direct
optimization of what is known as the {\it scale invariant Alpha-Beta
divergence} (sAB divergence). This new objective encompasses most variational
objectives that use the Kullback-Leibler, the R{\'e}nyi or the gamma
divergences. It also gives access to objective functions never exploited before
in the context of variational inference. This is achieved via two easy to
interpret control parameters, which allow for a smooth interpolation over the
divergence space while trading-off properties such as mass-covering of a target
distribution and robustness to outliers in the data. Furthermore, the sAB
variational objective can be optimized directly by repurposing existing methods
for Monte Carlo computation of complex variational objectives, leading to
estimates of the divergence instead of variational lower bounds. We show the
advantages of this objective on Bayesian models for regression problems.
