Convergence and Rate at the Budgets an Application Can Afford
Abstract
Convergence says how an allocation develops and rate analysis says how quickly under defined conditions. A practical assessment should include startup cost and near-tie alternatives over the actual operating budget range. Complete independent terminal checks supply performance evidence. A stable trace or a favorable asymptotic rate alone cannot justify the finite commitment. 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 and S. Gao, “Convergence Rate Analysis for Optimal Computing Budget Allocation Algorithms,” Automatica, vol. 153, 111042, 2023.
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.
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.
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.
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.
Published
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- 2026-10-15 (2)
- 2026-09-28 (1)