Approximating Model Equivalence in Interactive Dynamic Influence Diagrams Using Top K Policy Paths

Abstract

Interactive dynamic influence diagrams (I-DIDs) 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 behavioral models ascribed to other agents over time. Previous approaches mainly cluster behaviorally equivalent models to reduce the complexity of I-DID solutions. In this paper, we seek to further reduce the model space by introducing an approximate measure of behavioral equivalence (BE) and using it to group models. Specifically, we focus on $K$ most probable paths in the solution of each model and compare these policy paths to determine approximate BE. We discuss the challenges in computing the top $K$ policy paths and experimentally evaluate the performance of this heuristic approach in terms of the scalability and quality of the solution.