Constrained Best-Arm Learning with Uncertain Driving Inputs

Authors

  • Patrick Sullivan Author
  • Dominic Walters Author
  • Bradley Allen Author

Abstract

A constrained arm can appear admissible under a precisely estimated but inaccurate input distribution. Input-uncertain allocation distinguishes new evidence about inputs from new simulator replications. Evaluation should count both and independently assess the final joint requirement. A narrow conditional interval cannot make the driving model correct or guarantee performance outside represented inputs. 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

L. Yang, S. Gao, C. Li, and Y. Wang, “Stochastically Constrained Best Arm Identification with Thompson Sampling,” Automatica, vol. 176, 112223, 2025.

S. Gao, H. Xiao, E. Zhou, and W. Chen, “Optimal Computing Budget Allocation with Input Uncertainty,” Proceedings of the 2016 Winter Simulation Conference, pp. 839–846, 2016.

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.

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.

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Published

2025-05-30

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Articles