Finite-Time Error and the Limit of an Allocation Sequence

Authors

  • Brandon Hoffman Author
  • Alexander Turner Author
  • Dennis Matthews Author

Abstract

Finite-time knowledge-gradient analysis asks about decisions before the limit, whereas convergence analysis asks how an allocation develops. The useful comparison holds the decision objective fixed and reports initialization and complete-run uncertainty. A stable finite trace may be informative, but is not itself evidence for a convergence theorem or reliable stopping. 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. Y. Li and S. Gao, “On the Finite-Time Performance of the Knowledge Gradient Algorithm,” Proceedings of the 39th International Conference on Machine Learning, pp. 12741–12764, 2022.
  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. 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.
  6. Rasmussen, Carl Edward, and Christopher K. I. Williams. Gaussian Processes for Machine Learning. MIT Press, 2006. https://gaussianprocess.org/gpml/.
  7. 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.
  8. 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.
  9. 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.
  10. Glasserman, Paul. Monte Carlo Methods in Financial Engineering. Springer, 2004. https://doi.org/10.1007/978-0-387-21617-1.
  11. 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.
  12. 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.

Downloads

Published

2026-07-01

Versions

Issue

Vol. 2 No. 7 (2026): July 2026

Section

Articles