Approximate model equivalence for interactive dynamic influence diagrams
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Interactive dynamic influence diagrams (I-DIDs) graphically visualize a sequential decision problem for uncertain settings where multiple agents interact not only amongst themselves but also with the environment that they are in. Algorithms currently available for solving these I-DIDs face the issue of an exponentially growing candidate model space ascribed to the other agents, over time. One such algorithm identifies and prunes behaviorally equivalent models and replaces them with a representative thereby reducing the model space. 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 actionobservation paths, and introduce the notion of epsilon-subjective equivalence. We present a new approximation technique that uses our new definition of subjective equivalence to reduce the candidate model space by pruning models that are epsilon-subjectively equivalent with representative ones.