  In this paper,we consider the restless bandit problem, which is one of the
most well-studied generalizations of the celebrated stochastic multi-armed
bandit problem in decision theory. However, it is known be PSPACE-Hard to
approximate to any non-trivial factor. Thus the optimality is very difficult to
obtain due to its high complexity. A natural method is to obtain the greedy
policy considering its stability and simplicity. However, the greedy policy
will result in the optimality loss for its intrinsic myopic behavior generally.
In this paper, by analyzing one class of so-called standard reward function, we
establish the closed-form condition about the discounted factor \beta such that
the optimality of the greedy policy is guaranteed under the discounted expected
reward criterion, especially, the condition \beta = 1 indicating the optimality
of the greedy policy under the average accumulative reward criterion. Thus, the
standard form of reward function can easily be used to judge the optimality of
the greedy policy without any complicated calculation. Some examples in
cognitive radio networks are presented to verify the effectiveness of the
mathematical result in judging the optimality of the greedy policy.
