Relational Linear Programs
This work addresses the problem of representing and solving optimization problems over relational domains more intuitively for researchers and practitioners in AI and operations research, though it appears incremental as it builds on existing LP and logic programming techniques.
The authors introduced relational linear programming (RLP), a framework that combines linear programs with logic programs to declaratively define optimization problems over relational domains, enabling more intuitive representation and solving via lifted linear programming. They demonstrated its utility in experiments on approximate inference in Markov logic networks, solving Markov decision processes, and collective inference using LP support vector machines.
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.