A Constrained Arm inside a Partitioned Regression Domain

Authors

  • Matthew Bennett Author
  • Dominic Simmons Author
  • Anthony Matthews Author

Abstract

Constrained best-arm learning and partition regression organize feasibility evidence differently. Their comparison should preserve the same terminal admissibility requirement and check local boundary candidates independently. A partition can conceal an infeasible pocket, while posterior objective attraction can distract from unresolved constraints. Resource accounting should distinguish screening from precise objective comparison. 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. L. Yang, S. Gao, C. Li, and Y. Wang, “Stochastically Constrained Best Arm Identification with Thompson Sampling,” Automatica, vol. 176, 112223, 2025.
  2. F. Gao, S. Gao, H. Xiao, and Z. Shi, “Advancing Constrained Ranking and Selection with Regression in Partitioned Domains,” IEEE Transactions on Automation Science and Engineering, vol. 16, no. 1, pp. 382–391, 2019.
  3. 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.
  4. 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.
  5. Glasserman, Paul. Monte Carlo Methods in Financial Engineering. Springer, 2004. https://doi.org/10.1007/978-0-387-21617-1.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. Rasmussen, Carl Edward, and Christopher K. I. Williams. Gaussian Processes for Machine Learning. MIT Press, 2006. https://gaussianprocess.org/gpml/.

Downloads

Published

2025-12-02