  We introduce a framework for Bayesian experimental design (BED) with implicit
models, where the data-generating distribution is intractable but sampling from
it is still possible. In order to find optimal experimental designs for such
models, our approach maximises mutual information lower bounds that are
parametrised by neural networks. By training a neural network on sampled data,
we simultaneously update network parameters and designs using stochastic
gradient-ascent. The framework enables experimental design with a variety of
prominent lower bounds and can be applied to a wide range of scientific tasks,
such as parameter estimation, model discrimination and improving future
predictions. Using a set of intractable toy models, we provide a comprehensive
empirical comparison of prominent lower bounds applied to the aforementioned
tasks. We further validate our framework on a challenging system of stochastic
differential equations from epidemiology.
