Unknown Variance behind an Apparently Stable Allocation

Authors

  • Liam Butler Author
  • Jeffrey Turner Author
  • Scott Wheeler Author

Abstract

Unknown-variance ranking makes estimated precision part of the learning problem. A converging allocation trace can appear stable because an alternative stopped receiving observations. The test should vary pilots and inspect allocation starvation, then check the final decision independently. Consecutive estimates alone cannot distinguish learning from neglect. 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

  1. J. Du, S. Gao, and I. Ryzhov, “Revisiting an Open Question in Ranking and Selection under Unknown Variances,” Proceedings of the 2025 Winter Simulation Conference, pp. 378–389, 2025.
  2. Y. Li and S. Gao, “On the Convergence of Optimal Computing Budget Allocation Algorithms,” Proceedings of the 2021 Winter Simulation Conference, pp. 1–12, 2021.
  3. 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.
  4. Li, Y., Wang, H., Shang, X., Tang, X., Cao, Y., & Chen, X. (2026). BoostAPR: Boosting Automated Program Repair via Execution-Grounded Reinforcement Learning with Dual Reward Models. arXiv preprint arXiv:2605.09134.
  5. 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.
  6. 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.
  7. Rasmussen, Carl Edward, and Christopher K. I. Williams. Gaussian Processes for Machine Learning. MIT Press, 2006. https://gaussianprocess.org/gpml/.
  8. 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.
  9. 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.
  10. 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.
  11. Glasserman, Paul. Monte Carlo Methods in Financial Engineering. Springer, 2004. https://doi.org/10.1007/978-0-387-21617-1.
  12. 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.

Downloads

Published

2025-11-19

Versions

Issue

Vol. 1 No. 11 (2025): November 2025

Section

Articles