  Inventory control with unknown demand distribution is considered, with
emphasis placed on the case involving discrete nonperishable items. We focus on
an adaptive policy which in every period uses, as much as possible, the optimal
newsvendor ordering quantity for the empirical distribution learned up to that
period. The policy is assessed using the regret criterion, which measures the
price paid for ambiguity on demand distribution over $T$ periods. When there
are guarantees on the latter's separation from the critical newsvendor
parameter $\beta=b/(h+b)$, a constant upper bound on regret can be found.
Without any prior information on the demand distribution, we show that the
regret does not grow faster than the rate $T^{1/2+\epsilon}$ for any
$\epsilon>0$. In view of a known lower bound, this is almost the best one could
hope for. Simulation studies involving this along with other policies are also
conducted.
