Epsilon-Subjective Equivalence of Models for Interactive Dynamic Influence Diagrams

Abstract

Interactive dynamic influence diagrams (I-DID) are graphical models for sequential decision making in uncertain settings shared by other agents. Algorithms for solving I-DIDs face the challenge of an exponentially growing space of candidate models ascribed to other agents, over time. Pruning behaviorally equivalent models is one way toward minimizing the model set. We seek to further reduce the complexity by additionally pruning models that are approximately subjectively equivalent. Toward this, we define subjective equivalence in terms of the distribution over the subject agent's future action-observation paths, and introduce the notion of epsilon-subjective equivalence. We present a new approximation technique that reduces the candidate model space by removing models that are epsilon-subjectively equivalent with representative ones.