Efficient Learning for Clustering and Optimizing Context-Dependent Designs

We consider a simulation optimization problem for a context-dependent decision-making. A Gaussian mixture model is proposed to capture the performance clustering phenomena of context-dependent designs. Under a Bayesian framework, we develop a dynamic sampling policy to efficiently learn both the global information of each cluster and local information of each design for selecting the best designs in all contexts. The proposed sampling policy is proved to be consistent and achieve the asymptotically optimal sampling ratio. Numerical experiments show that the proposed sampling policy significantly improves the efficiency in context-dependent simulation optimization.