  We consider a distributionally robust Partially Observable Markov Decision
Process (DR-POMDP), where the distribution of the transition-observation
probabilities is unknown at the beginning of each decision period, but their
realizations can be inferred using side information at the end of each period
after an action being taken. We build an ambiguity set of the joint
distribution using bounded moments via conic constraints and seek an optimal
policy to maximize the worst-case (minimum) reward for any distribution in the
set. We show that the value function of DR-POMDP is piecewise linear convex
with respect to the belief state and propose a heuristic search value iteration
method for obtaining lower and upper bounds of the value function. We conduct
numerical studies and demonstrate the computational performance of our approach
via testing instances of a dynamic epidemic control problem. Our results show
that DR-POMDP can produce more robust policies under misspecified distributions
of transition-observation probabilities as compared to POMDP, but has less
costly solutions than robust POMDP. The DR-POMDP policies are also insensitive
to varying parameter in the ambiguity set and to noise added to the true
transition-observation probability values obtained at the end of each decision
period.
