We develop new graphical representations for the problem of sequential decision making in partially observable multiagent environments, as formalized by interactive partially observable Markov decision processes (I-POMDPs). The graphical models called interactive inf uence diagrams (I-IDs) and their dynamic counterparts, interactive dynamic inf uence diagrams (I-DIDs), seek to explicitly model the structure that is often present in real-world problems by decomposing the situation into chance and decision variables, and the dependencies between the variables. I-DIDs generalize DIDs, which may be viewed as graphical representations of POMDPs, to multiagent settings in the same way that IPOMDPs generalize POMDPs. I-DIDs may be used to compute the policy of an agent given its belief as the agent acts and observes in a setting that is populated by other interacting agents. Using several examples, we show how I-IDs and I-DIDs may be applied and demonstrate their usefulness. We also show how the models may be solved using the standard algorithms that are applicable to DIDs. Solving I-DIDs exactly involves knowing the solutions of possible models of the other agents. The space of models grows exponentially with the number of time steps. We present a method of solving I-DIDs approximately by limiting the number of other agents’ candidate models at each time step to a constant. We do this by clustering models that are likely to be behaviorally equivalent and selecting a representative set from the clusters. We discuss the error bound of the approximation technique and demonstrate its empirical performance.
Bibliographical noteAuthor can archive post-print (ie final draft post-refereeing).
Doshi, P., Zeng, Y., & Chen, Q. (2008). Graphical models for interactive POMDPs: representations and solutions. Autonomous Agents and Multi-Agent Systems, 18(3), 376-416. https://doi.org/10.1007/s10458-008-9064-7