Relational Linear Programs

TL;DR

This paper introduces relational linear programming (RLP), a framework combining LPs and logic programming to efficiently model and solve optimization problems over relational data, leveraging symmetries for computational gains.

Contribution

The paper presents RLP, a novel declarative framework that integrates logical concepts with linear programming, enabling scalable and intuitive modeling of relational optimization problems.

Findings

Effective in approximate inference for Markov logic networks

Successfully applied to Markov decision processes

Improves efficiency through lifted linear programming

Abstract

We propose relational linear programming, a simple framework for combing linear programs (LPs) and logic programs. A relational linear program (RLP) is a declarative LP template defining the objective and the constraints through the logical concepts of objects, relations, and quantified variables. This allows one to express the LP objective and constraints relationally for a varying number of individuals and relations among them without enumerating them. Together with a logical knowledge base, effectively a logical program consisting of logical facts and rules, it induces a ground LP. This ground LP is solved using lifted linear programming. That is, symmetries within the ground LP are employed to reduce its dimensionality, if possible, and the reduced program is solved using any off-the-shelf LP solver. In contrast to mainstream LP template languages like AMPL, which features a mixture of declarative and imperative programming styles, RLP's relational nature allows a more intuitive representation of optimization problems over relational domains. We illustrate this empirically by experiments on approximate inference in Markov logic networks using LP relaxations, on solving Markov decision processes, and on collective inference using LP support vector machines.