  Deciding how to act in partially observable environments remains an active
area of research. Identifying good sequences of decisions is particularly
challenging when good control performance requires planning multiple steps into
the future in domains with many states. Towards addressing this challenge, we
present an online, forward-search algorithm called the Posterior Belief
Distribution (PBD). PBD leverages a novel method for calculating the posterior
distribution over beliefs that result after a sequence of actions is taken,
given the set of observation sequences that could be received during this
process. This method allows us to efficiently evaluate the expected reward of a
sequence of primitive actions, which we refer to as macro-actions. We present a
formal analysis of our approach, and examine its performance on two very large
simulation experiments: scientific exploration and a target monitoring domain.
We also demonstrate our algorithm being used to control a real robotic
helicopter in a target monitoring experiment, which suggests that our approach
has practical potential for planning in real-world, large partially observable
domains where a multi-step lookahead is required to achieve good performance.
