POMDP is considered as a basic model for decision making under uncertainty.As a generalization of the exact POMDP model,the boundedparameter POMDP (BPOMDP) provides only upper and lower bounds on the state-transition probabilities,observation probabilities and rewards,which is particularly suitable for characterizing the situations where the underlying model is imprecisely given or time-varying.This paper presents the optimistic criterion for optimality for solving BPOMDPs,under which the optimistically optimal value function is defined.By representing a policy explicitly as a finite-state controller,we propose a policy iteration approach that is shown to converge to an e-optimal policy under the optimistic optimality criterion.