CO-BED: Information-Theoretic Contextual Optimization via Bayesian Experimental Design

TL;DR

CO-BED introduces a versatile, information-theoretic framework for contextual optimization using Bayesian experimental design, employing variational methods and continuous relaxations to handle diverse action spaces effectively.

Contribution

It presents a novel, model-agnostic approach that unifies Bayesian experimental design with variational optimization for contextual experiments.

Findings

Demonstrates competitive performance across various experiments.

Provides a general framework adaptable to different models and action types.

Achieves effective optimization with a single stochastic gradient scheme.

Abstract

We formalize the problem of contextual optimization through the lens of Bayesian experimental design and propose CO-BED -- a general, model-agnostic framework for designing contextual experiments using information-theoretic principles. After formulating a suitable information-based objective, we employ black-box variational methods to simultaneously estimate it and optimize the designs in a single stochastic gradient scheme. In addition, to accommodate discrete actions within our framework, we propose leveraging continuous relaxation schemes, which can naturally be integrated into our variational objective. As a result, CO-BED provides a general and automated solution to a wide range of contextual optimization problems. We illustrate its effectiveness in a number of experiments, where CO-BED demonstrates competitive performance even when compared to bespoke, model-specific alternatives.