Bayesian models quantify uncertainty and facilitate optimal decision-making in downstream applications. For most models, however, practitioners are forced to use approximate inference techniques that lead to sub-optimal decisions due to incorrect posterior predictive distributions. We present a novel approach that corrects for inaccuracies in posterior inference by altering the decision-making process. We train a separate model to make optimal decisions under the approximate posterior, combining interpretable Bayesian modeling with optimization of direct predictive accuracy in a principled fashion. The solution is generally applicable as a plug-in module for predictive decision-making for arbitrary probabilistic programs, irrespective of the posterior inference strategy. We demonstrate the approach empirically in several problems, confirming its potential.

Bayesian decision theory outlines a rigorous framework for making optimal decisions based on maximizing expected utility over a model posterior. However, practitioners often do not have access to the full posterior and resort to approximate inference strategies. In such cases, taking the eventual decision-making task into account while performing the inference allows for calibrating the posterior approximation to maximize the utility. We present an automatic pipeline that co-opts continuous utilities into variational inference algorithms to account for decision-making. We provide practical strategies for approximating and maximizing the gain, and empirically demonstrate consistent improvement when calibrating approximations for specific utilities.