Optimal stopping and dynamic allocation

A class of optimal stopping problems for the Wiener process is studied herein, and asymptotic expansions for the optimal stopping boundaries are derived. These results lead to a simple index-type class of asymptotically optimal solutions to the classical discounted multi-armed bandit problem: given a discount factor 0<. <1 and k populations with densities from an exponential family, how should x1, x2,. be sampled sequentially from these populations to maximize the expected value of ..1 .i.1xi, in ignorance of the parameters of the densities?