  Molecular optimization aims to discover novel molecules with desirable
properties. Two fundamental challenges are: (i) it is not trivial to generate
valid molecules in a controllable way due to hard chemical constraints such as
the valency conditions, and (ii) it is often costly to evaluate a property of a
novel molecule, and therefore, the number of property evaluations is limited.
These challenges are to some extent alleviated by a combination of a
variational autoencoder (VAE) and Bayesian optimization (BO). VAE converts a
molecule into/from its latent continuous vector, and BO optimizes a latent
continuous vector (and its corresponding molecule) within a limited number of
property evaluations. While the most recent work, for the first time, achieved
100% validity, its architecture is rather complex due to auxiliary neural
networks other than VAE, making it difficult to train. This paper presents a
molecular hypergraph grammar variational autoencoder (MHG-VAE), which uses a
single VAE to achieve 100% validity. Our idea is to develop a graph grammar
encoding the hard chemical constraints, called molecular hypergraph grammar
(MHG), which guides VAE to always generate valid molecules. We also present an
algorithm to construct MHG from a set of molecules.
