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.