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A Sufficient Statistic for Influence in Structured Multiagent Environments

Frans A. Oliehoek, Stefan Witwicki, and Leslie P. Kaelbling. A Sufficient Statistic for Influence in Structured Multiagent Environments. Journal of Artificial Intelligence Research, pp. 789–870, AI Access Foundation, Inc., February 2021.

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Abstract

Making decisions in complex environments is a key challenge in artificial intelligence (AI).Situations involving multiple decision makers are particularly complex, leading to compu-tational intractability of principled solution methods. A body of work in AI has tried tomitigate this problem by trying to distill interaction to its essence: how does the policy ofone agent influence another agent? If we can find more compact representations of suchinfluence, this can help us deal with the complexity, for instance by searching the spaceof influences rather than the space of policies. However, so far these notions of influencehave been restricted in their applicability to special cases of interaction. In this paper weformalize influence-based abstraction (IBA), which facilitates the elimination of latent statefactors without any loss in value, for a very general class of problems described as factoredpartially observable stochastic games (fPOSGs). On the one hand, this generalizes existingdescriptions of influence, and thus can serve as the foundation for improvements in scala-bility and other insights in decision making in complex multiagent settings. On the otherhand, since the presence of other agents can be seen as a generalization of single agent set-tings, our formulation of IBA also provides a sufficient statistic for decision making underabstraction for a single agent. We also give a detailed discussion of the relations to suchprevious works, identifying new insights and interpretations of these approaches. In theseways, this paper deepens our understanding of abstraction in a wide range of sequentialdecision making settings, providing the basis for new approaches and algorithms for a largeclass of problems.

BibTeX Entry

@ARTICLE{Oliehoek21JAIR,
       author = {{Oliehoek}, Frans A. and {Witwicki}, Stefan and {Kaelbling}, Leslie P.},
        title = {A Sufficient Statistic for Influence in Structured Multiagent Environments},
      journal = JAIR,
         year = 2021,
        month = feb,
    publisher = {AI Access Foundation, Inc.},
        doi   = {10.1613/jair.1.12136},
        url   = {https://doi.org/10.1613/jair.1.12136},
        pages = {789--870},
    keywords =   {refereed},
    abstract = {
Making decisions in complex environments is a key challenge in artificial intelligence (AI).
Situations involving multiple decision makers are particularly complex, leading to compu-
tational intractability of principled solution methods. A body of work in AI has tried to
mitigate this problem by trying to distill interaction to its essence: how does the policy of
one agent influence another agent? If we can find more compact representations of such
influence, this can help us deal with the complexity, for instance by searching the space
of influences rather than the space of policies. However, so far these notions of influence
have been restricted in their applicability to special cases of interaction. In this paper we
formalize influence-based abstraction (IBA), which facilitates the elimination of latent state
factors without any loss in value, for a very general class of problems described as factored
partially observable stochastic games (fPOSGs). On the one hand, this generalizes existing
descriptions of influence, and thus can serve as the foundation for improvements in scala-
bility and other insights in decision making in complex multiagent settings. On the other
hand, since the presence of other agents can be seen as a generalization of single agent set-
tings, our formulation of IBA also provides a sufficient statistic for decision making under
abstraction for a single agent. We also give a detailed discussion of the relations to such
previous works, identifying new insights and interpretations of these approaches. In these
ways, this paper deepens our understanding of abstraction in a wide range of sequential
decision making settings, providing the basis for new approaches and algorithms for a large
class of problems.        
    }
}

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