  Real-world optimization problems are generally not just black-box problems,
but also involve mixed types of inputs in which discrete and continuous
variables coexist. Such mixed-space optimization possesses the primary
challenge of modeling complex interactions between the inputs. In this work, we
propose a novel yet simple approach that entails exploiting the graph data
structure to model the underlying relationship between variables, i.e.,
variables as nodes and interactions defined by edges. Then, a variational graph
autoencoder is used to naturally take the interactions into account. We first
provide empirical evidence of the existence of such graph structures and then
suggest a joint framework of graph structure learning and latent space
optimization to adaptively search for optimal graph connectivity. Experimental
results demonstrate that our method shows remarkable performance, exceeding the
existing approaches with significant computational efficiency for a number of
synthetic and real-world tasks.
