  Optimization in the latent space of variational autoencoders is a promising
approach to generate high-dimensional discrete objects that maximize an
expensive black-box property (e.g., drug-likeness in molecular generation,
function approximation with arithmetic expressions). However, existing methods
lack robustness as they may decide to explore areas of the latent space for
which no data was available during training and where the decoder can be
unreliable, leading to the generation of unrealistic or invalid objects. We
propose to leverage the epistemic uncertainty of the decoder to guide the
optimization process. This is not trivial though, as a naive estimation of
uncertainty in the high-dimensional and structured settings we consider would
result in high estimator variance. To solve this problem, we introduce an
importance sampling-based estimator that provides more robust estimates of
epistemic uncertainty. Our uncertainty-guided optimization approach does not
require modifications of the model architecture nor the training process. It
produces samples with a better trade-off between black-box objective and
validity of the generated samples, sometimes improving both simultaneously. We
illustrate these advantages across several experimental settings in digit
generation, arithmetic expression approximation and molecule generation for
drug design.
