A Partition Search under Worst-Case Admissibility
Abstract
Regional sample allocation and worst-case constraints can direct evidence toward different locations. The evaluation should identify whether a run discovers alternatives, refines nominal performance, or checks an adverse scenario. Independent final outcomes preserve joint admissibility. A promising discovered region remains incomplete evidence if the protected feasibility boundary was never directly assessed. This focused synthesis develops an empirical comparison that preserves the terminal action, observation process, and total verification cost. Its proposed tests are prospective; no new simulation run, model-training result, or intervention effect is reported.
References
Z. Shi, S. Gao, H. Xiao, and W. Chen, “A Worst-Case Formulation for Constrained Ranking and Selection with Input Uncertainty,” Naval Research Logistics, vol. 66, pp. 648–662, 2019.
W. Chen, S. Gao, C.-H. Chen, and L. Shi, “An Optimal Sample Allocation Strategy for Partition-Based Random Search,” IEEE Transactions on Automation Science and Engineering, vol. 11, pp. 177–186, 2014.
Kim, Seong-Hee, and Barry L. Nelson. “A Fully Sequential Procedure for Indifference-Zone Selection in Simulation.” ACM Transactions on Modeling and Computer Simulation, vol. 11, no. 3, 2001, pp. 251–273. https://doi.org/10.1145/502109.502111.
Chick, Stephen E., and Koichiro Inoue. “New Two-Stage and Sequential Procedures for Selecting the Best Simulated System.” Operations Research, vol. 49, no. 5, 2001, pp. 732–743. https://doi.org/10.1287/opre.49.5.732.10615.
Frazier, Peter I., Warren B. Powell, and Savas Dayanik. “A Knowledge-Gradient Policy for Sequential Information Collection.” SIAM Journal on Control and Optimization, vol. 47, no. 5, 2008, pp. 2410–2439. https://doi.org/10.1137/070693424.
Rasmussen, Carl Edward, and Christopher K. I. Williams. Gaussian Processes for Machine Learning. MIT Press, 2006. https://gaussianprocess.org/gpml/.
Sacks, Jerome, William J. Welch, Toby J. Mitchell, and Henry P. Wynn. “Design and Analysis of Computer Experiments.” Statistical Science, vol. 4, no. 4, 1989, pp. 409–423. https://doi.org/10.1214/ss/1177012413.
Bertsimas, Dimitris, and Melvyn Sim. “The Price of Robustness.” Operations Research, vol. 52, no. 1, 2004, pp. 35–53. https://doi.org/10.1287/opre.1030.0065.
Campi, Marco C., and Simone Garatti. “The Exact Feasibility of Randomized Solutions of Uncertain Convex Programs.” SIAM Journal on Optimization, vol. 19, no. 3, 2008, pp. 1211–1230. https://doi.org/10.1137/07069821X.
Glasserman, Paul. Monte Carlo Methods in Financial Engineering. Springer, 2004. https://doi.org/10.1007/978-0-387-21617-1.