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.

Originality: The paper builds on ideas developed by Lacoste-Julien et al. (2011) that were introduced to bridge Bayesian decision theory with approximate inference in a meaningful and useful way. The paper takes these ideas and makes them applicable in continuously-valued settings so long as the losses are bounded. For inference, it uses a variation of'black box' type variational inference schemes. Quality: The paper makes an interesting contribution. However, it is undesirable that the losses must be bounded.

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.

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. Papers published at the Neural Information Processing Systems Conference.

A considerable proportion of research on Bayesian machine learning concerns itself with the fundamental task of inference, developing techniques for an efficient and accurate approximation of the posterior distribution p(θ D) of the model parameters θ conditional on observed data D. However, in most cases, this is not the end goal in itself. Instead, we eventually want to solve a decision problem of some kind and merely use the posterior distribution as a summary of the information provided by the data and the modeling assumptions. For example, we may want to decide to automatically shut down a process to avoid costs associated with its potential failure, yet might not necessarily care about whether we model all aspects of the process accurately. The focus on inference is justified by Bayesian decision theory Berger (1985). It formalizes the notion that the posterior distribution is sufficient for making optimal decisions under a utility. This is achieved by selecting decisions that maximize the expected utility, computed by integrating over the posterior.