Treffer: Efficient Learning for Clustering and Optimizing Context-Dependent Designs.

Contextual simulation optimization problems have attracted great attention in the healthcare, commercial, and financial fields because of the need for personalized decision making. Besides randomness in simulation outputs, larger solution space makes learning and optimization more challenging. In the current work, Li, Lam, and Peng use a Gaussian mixture model (GMM) as a basic technique to deal with this difficulty. To address the computational challenge in updating GMM-based Bayesian posterior, they present a computationally efficient approximation method that can reduce the computational complexity from an exponential rate to a linear rate with respect to the problem scale. For sample allocation decision making, they propose a dynamic sampling policy to efficiently utilize both global clustering information and local performance information. The proposed sampling policy is proved to be consistent, be implementable, and achieve the asymptotically optimal sampling ratio. Numerical experiments show that the proposed sampling policy significantly improves the efficiency in contextual simulation optimization. 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. [ABSTRACT FROM AUTHOR]

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