Efficient Learning for Clustering and Optimizing Context-Dependent Designs

We consider a simulation optimization problem for context-dependent decision making. Under a Gaussian mixture model-based Bayesian framework, we develop a dynamic sampling policy to maximize the worst-case probability of correctly selecting the best design over all contexts, which utilizes both global clustering information and local performance information. In particular, we design a computationally efficient approximation method to learn these sources of information, thereby leading to an implementable dynamic sampling policy. The proposed sampling policy is proved to be consistent and achieve the asymptotically optimal sampling ratio. Numerical experiments show that the proposed approximation method makes a good balance between the performance and complexity, and the proposed sampling policy significantly improves the efficiency in context-dependent simulation optimization.

Funding: This work was supported in part by the National Natural Science Foundation of China [Grants 72022001, 92146003, and 71901003], by the National Science Foundation [Awards ECCS-1462409, CMMI-1462787, CAREER CMMI-1834710, and IIS-1849280], and by the China Scholarship Council [scholarship under Grant China Scholarship Council].

Supplemental Material: The e-companion is available at https://doi.org/10.1287/opre.2022.2368.