Variational Bayesian Decision-making for Continuous Utilities
This work addresses a practical challenge in Bayesian decision-making for practitioners who rely on approximate inference, offering a method to enhance utility maximization in specific applications.
The paper tackles the problem of making optimal decisions when only approximate posterior distributions are available, by integrating continuous utilities into variational inference to calibrate approximations for specific decision-making tasks, and empirically shows consistent improvement.
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.