  Partially observable Markov decision processes (POMDPs) provide a principled
framework for sequential planning in uncertain single agent settings. An
extension of POMDPs to multiagent settings, called interactive POMDPs
(I-POMDPs), replaces POMDP belief spaces with interactive hierarchical belief
systems which represent an agent's belief about the physical world, about
beliefs of other agents, and about their beliefs about others' beliefs. This
modification makes the difficulties of obtaining solutions due to complexity of
the belief and policy spaces even more acute. We describe a general method for
obtaining approximate solutions of I-POMDPs based on particle filtering (PF).
We introduce the interactive PF, which descends the levels of the interactive
belief hierarchies and samples and propagates beliefs at each level. The
interactive PF is able to mitigate the belief space complexity, but it does not
address the policy space complexity. To mitigate the policy space complexity --
sometimes also called the curse of history -- we utilize a complementary method
based on sampling likely observations while building the look ahead
reachability tree. While this approach does not completely address the curse of
history, it beats back the curse's impact substantially. We provide
experimental results and chart future work.
