Lifted Optimization for Relational Preference Rules

The move to relational probabilistic models from propositional models stemmed from the realization that the type of knowledge we have and need in many domains is at a level more generic than that of concrete objects. In reasoning about preference, too, often we have knowledge about the desirable behavior or state of a system of agents/objects, that applies to different instantiations of this system, while instantiations may differ in the number and properties of concrete objects. As an example, imagine the problem of monitoring emergency services in a large city. Our objects are fire-fighters, fire-engines, fire-events, injured civilians, and various devices that help us monitor the state of this system, such as cameras and other mounted and stationary sensors. These instruments transmit huge amounts of data to a control center, and our system must decide which information (e.g., which video streams) to display to a decision-maker monitoring this system at each point in time. As the set of objects and their properties change across time (e.g., as new fire events occur), the logic behind what is desirable and what is less desirable can (and must) be described at a generic level, so that it will apply to different concrete instances of such a monitoring system. In Brafman [2008] we proposed relational preference rules (RPR) as a formalism for modeling preference/value information about such a system. RPRs are similar in form to existing PRMs, such as Bayesian Logic [Kersting and Raedt, 2007], Relational Bayesian Networks [Jaeger, 1997], and Markov Logic [Richardson and Domingos, 2006], and can be viewed as relational UCP networks Boutilier et al. [2001], which induce a GAI value function over any given set of objects. We illustrate the basics of this formalism here, and refer the reader to Brafman [2008] for more details. In this paper we concentrate on lifted inference for relational preference rules which turns out to be quite different from lifted probabilistic inference rules.