  We investigate partially observed Markov decision processes (POMDPs) with
cost functions regularized by entropy terms describing state, observation, and
control uncertainty. Standard POMDP techniques are shown to offer bounded-error
solutions to these entropy-regularized POMDPs, with exact solutions possible
when the regularization involves the joint entropy of the state, observation,
and control trajectories. Our joint-entropy result is particularly surprising
since it constitutes a novel, tractable formulation of active state estimation.
