  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.
