  The J-choice K-best secretary problem, also known as the (J,K)-secretary
problem, is a generalization of the classical secretary problem. An algorithm
for the (J,K)-secretary problem is allowed to make J choices and the payoff to
be maximized is the expected number of items chosen among the K best items.
  Previous works analyzed the case when the total number n of items is finite,
and considered what happens when n grows. However, for general J and K, the
optimal solution for finite n is difficult to analyze. Instead, we prove a
formal connection between the finite model and the infinite model, where there
are countably infinite number of items, each attached with a random arrival
time drawn independently and uniformly from [0,1].
  We use primal-dual continuous linear programming techniques to analyze a
class of infinite algorithms, which are general enough to capture the
asymptotic behavior of the finite model with large number of items. Our
techniques allow us to prove that the optimal solution can be achieved by the
(J,K)-Threshold Algorithm, which has a nice "rational description" for the case
K = 1.
