Learning to satisfy

This paper investigates a class of learning problems called learning satisfiability (LSAT) problems, where the goal is to learn a set in the input (feature) space that satisfies a number of desired output (label/response) constraints. LSAT problems naturally arise in many applications in which one is interested in the class of inputs that produce desirable outputs, rather than simply a single optimum. A distinctive aspect of LSAT problems is that the output behavior is assessed only on the solution set, whereas in most statistical learning problems output behavior is evaluated over the entire input space. We present a novel support vector machine (SVM) algorithm for solving LSAT problems and apply it to a synthetic data set to illustrate the impact of the LSAT formulation.