  Many real-life decision-making situations allow further relevant information
to be acquired at a specific cost, for example, in assessing the health status
of a patient we may decide to take additional measurements such as diagnostic
tests or imaging scans before making a final assessment. Acquiring more
relevant information enables better decision making, but may be costly. How can
we trade off the desire to make good decisions by acquiring further information
with the cost of performing that acquisition? To this end, we propose a
principled framework, named EDDI (Efficient Dynamic Discovery of high-value
Information), based on the theory of Bayesian experimental design. In EDDI, we
propose a novel partial variational autoencoder (Partial VAE) to predict
missing data entries problematically given any subset of the observed ones, and
combine it with an acquisition function that maximizes expected information
gain on a set of target variables. We show cost reduction at the same decision
quality and improved decision quality at the same cost in multiple machine
learning benchmarks and two real-world health-care applications.
