Structured Learning Modulo Theories
  Modelling problems containing a mixture of Boolean and numerical variables is
a long-standing interest of Artificial Intelligence. However, performing
inference and learning in hybrid domains is a particularly daunting task. The
ability to model this kind of domains is crucial in "learning to design" tasks,
that is, learning applications where the goal is to learn from examples how to
perform automatic {\em de novo} design of novel objects. In this paper we
present Structured Learning Modulo Theories, a max-margin approach for learning
in hybrid domains based on Satisfiability Modulo Theories, which allows to
combine Boolean reasoning and optimization over continuous linear arithmetical
constraints. The main idea is to leverage a state-of-the-art generalized
Satisfiability Modulo Theory solver for implementing the inference and
separation oracles of Structured Output SVMs. We validate our method on
artificial and real world scenarios.
