Randomized allocation with nonparametric estimation for a multi-armed bandit problem with covariates

Annals of Statistics

Volumn 30, Issue 1, 2002, Pages 100-121

  Yang, Yuhong ^a   Zhu, Dan ^a  

^a Iowa State University   (United States)

Author keywords

Concomitant variable; Multi armed bandits; Nonparametric regression; Randomized allocation; Sequential allocation

Indexed keywords

EID: 0036108219     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1015362186     Document Type: Article

References (20)

1. AUER, P., CESA-BIANCHI, N., FREUND, Y. and SCHAPIRE, R. E. (1995). Gambling in a rigged casino: the adversarial multi-armed bandit problem. In 36th Annual Symposium on Foundations of Computer Science 322-331. IEEE Computer Society Press, Los Alamitos, CA.
2. BERRY, D. A., CHEN, R. W., ZAME, A., HEATH, D. C. and SHEPP, L. A. (1997). Bandit problems with infinitely many arms. Ann. Statist. 25 2103-2116.
3. BERRY, D. A. and FRISTEDT, B. (1985). Bandit Problems: Sequential Allocation of Experiments. Chapman and Hall, New York.
4. BIRGÉ, L. and MASSART, P. (1998). Minimum contrast estimators on sieves: exponential bounds and rates of convergence. Bernoulli 4 329-375.
5. CLAYTON, M. K. (1989). Covariate models for Bernoulli bandits. Sequential Anal. 8 405-426.
6. 1 error of partitioning estimates of a regression function. In Proceedings of the Fourth Pannonian Symposium on Mathematical Statistics (F. Konecny, J. Mogyoródi and W. Wertz, eds.) 67-76. Akadémiai Kiadó, Budapest.
7. DEVROYE, L., GYÖRFI, L., KRZYZAK, A. and LUGOSI, G. (1994). On the strong universal consistency of nearest neighbor regression function estimates. Ann. Statist. 22 1371-1385.
8. DEVROYE, L., GYÖRFI, L. and LUGOSI, G. (1996). A Probabilistic Theory of Pattern Recognition. Springer, New York.
9. FAN, J. and GIJBELS, I. (1996). Local Polynomial Modeling and Its Applications. Chapman and Hall, New York.
10. GITTINS, J. C. (1989). Multi-armed Bandit Allocation Indices. Wiley, New York.
11. GRATCH, J., DEJONG, G. and YANG, Y. (1994). Rational learning: finding a balance between utility and efficiency. Selecting Models from Data: Artificial Intelligence and Statistics. Lecture Notes in Statist. 89 11-20. Springer, New York.
12. LAI, T. L. and ROBBINS, H. (1985). Asymptotically efficient adaptive allocation rules. Adv. In Appl. Math. 6 4-22.
13. LAI, T. L. and YAKOWITZ, S. (1995). Machine learning and nonparametric bandit theory. IEEE Trans. Automat. Control 40 1199-1209.
14. NOBEL, A. (1996). Histogram regression estimation using data-dependent partitions. Ann. Statist. 24 1084-1105.
15. POLLARD, D. (1984). Convergence of Stochastic Processes. Springer, New York.
16. ROBBINS, H. (1952). Some aspects of the sequential design of experiments. Bull. Amer. Math. Soc. 58 527-535.
17. SARKAR, J. (1991). One-armed bandit problems with covariates. Ann. Statist. 19 1978-2002.
18. STONE, C. S. (1977). Consistent nonparametric regression. Ann. Statist. 5 595-620.
19. VAN DER VAART, A. W. and WELLNER, J. A. (1996). Weak Convergence and Empirical Processes: With Applications to Statistics. Springer, New York.
20. WOODROOFE, M. (1979). A one-armed bandit problem with a concomitant variable. J. Amer. Statist. Assoc. 74 799-806.