Large Deviations Perspective on Ordinal Optimization of Heavy-tailed Systems

We consider the problem of selecting the best among several heavy-tailed systems from a large deviations perspective. In contrast to the light-tailed setting studied by Glynn and Juneja (2004), in the heavy-tailed setting, the probability of false selection is characterized by a rate function that does not require as detailed information about the probability distributions of the system's performance. This motivates the question of studying static policies that could potentially provide convenient implementations in heavy-tailed settings. We concentrate on studying sharp large deviations estimates for the probability of false detection which suggest precise optimal allocation policies when the systems have comparable heavy-tails. Additional optimality insights are given for systems with non-comparable tails.