Structured Learning Modulo Theories

TL;DR

This paper introduces Structured Learning Modulo Theories, a max-margin framework that combines Boolean reasoning and continuous optimization using Satisfiability Modulo Theories to enable learning in hybrid domains involving both Boolean and numerical variables.

Contribution

It presents a novel approach integrating Satisfiability Modulo Theories with Structured Output SVMs for hybrid domain learning, leveraging advanced SMT solvers for inference and separation.

Findings

Effective in artificial scenarios

Successful on real-world applications

Outperforms existing methods in hybrid domain tasks

Abstract

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.