Speeding Up Exact Solutions of Interactive Dynamic Influence Diagrams Using Action Equivalence

Interactive dynamic influence diagrams (I-DIDs) are graphical models for sequential decision making in partially observable 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. Previous approach for exactly solving I-DIDs groups together models having similar solutions into behaviorally equivalent classes and updates these classes. We present a new method that, in addition to aggregating behaviorally equivalent models, further groups models that prescribe identical actions at a single time step. We show how to update these augmented classes and prove that our method is exact. The new approach enables us to bound the aggregated model space by the cardinality of other agents' actions. We evaluate its performance and provide empirical results in support.