  We consider the problem of approximate belief-state monitoring using particle
filtering for the purposes of implementing a policy for a partially-observable
Markov decision process (POMDP). While particle filtering has become a
widely-used tool in AI for monitoring dynamical systems, rather scant attention
has been paid to their use in the context of decision making. Assuming the
existence of a value function, we derive error bounds on decision quality
associated with filtering using importance sampling. We also describe an
adaptive procedure that can be used to dynamically determine the number of
samples required to meet specific error bounds. Empirical evidence is offered
supporting this technique as a profitable means of directing sampling effort
where it is needed to distinguish policies.
