Ordinal Optimization with Generalized Linear Model

Given a number of stochastic systems, we consider an ordinal optimization problem to find an optimal allocation of a finite sampling budget, which maximizes the likelihood of selecting the "best" system, where the "best" is defined as the one with the highest mean. The statistical characteristics of each system are described by the generalized linear model, where unknown parameters are estimated using maximum likelihood estimation. To formulate the problem in a tractable form, we use the large deviations theory to characterize the structural properties of the optimal allocation. Further, motivated by Euclidean information theory, we obtain an approximate solution for the optimal allocation, which is leveraged to design a sampling strategy that is near-optimal in a suitable asymptotic sense. The proposed sampling strategy is computationally tractable, and we show via numerical testing that it performs competitively even in the presence of model misspecification.