Myopic Replication in a Search Space That Is Still Expanding
Abstract
Partition allocation can purchase new regional coverage, while a myopic ranking procedure refines a local comparison. Their value depends on what remains uncertain about the final action. Evaluation should record discovery and replication separately and reserve terminal checks. Long-run allocation quality within a known list does not establish adequate search coverage. 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
Y. Li, S. Gao, and T. Shi, “Asymptotic Optimality of Myopic Ranking and Selection Procedures,” Automatica, vol. 151, 110896, 2023.
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.
Zhou, Yongxi, Lai Yun Choi, Jiaxi Wen, Wenbo Ye, and Junwei Yao. “How Much Can Repeated Running Buy? A Measured Variance Ceiling for LLM Code Evaluation.” arXiv, 2026, arXiv:2606.00920. https://arxiv.org/abs/2606.00920.
Glasserman, Paul. Monte Carlo Methods in Financial Engineering. Springer, 2004. https://doi.org/10.1007/978-0-387-21617-1.
Ankenman, Bruce, Barry L. Nelson, and Jeremy Staum. “Stochastic Kriging for Simulation Metamodeling.” Operations Research, vol. 58, no. 2, 2010, pp. 371–382. https://doi.org/10.1287/opre.1090.0754.
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.
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- 2026-10-15 (2)
- 2026-05-09 (1)