A note on performance limitations in bandit problems with side information

IEEE Transactions on Information Theory

Volumn 57, Issue 3, 2011, Pages 1707-1713

  Goldenshluger, Alexander ^a   Zeevi, Assaf ^b  

^a UNIVERSITY OF HAIFA   (Israel)

^b Och Spine at New York Presbyterian Hospitals   (United States)

Author keywords

Allocation rule; inferior sampling rate; lower bound; side information; two armed bandit

Indexed keywords

ALLOCATION RULE; INFERIOR SAMPLING RATE; LOWER BOUND; SIDE INFORMATION; TWO-ARMED BANDIT;

RANDOM VARIABLES;

EID: 79951890373     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2011.2104450     Document Type: Article

References (20)

1. P. Auer, N. Cesa-Bianchi, and P. Fischer, "Finite time analysis of the multiarmed bandit problem," Mach. Learn., vol. 47, pp. 235-256, 2002. (Pubitemid 34126111)
2. V. Anantharam, P. Varaiya, and J. Warland, "Asymptotically efficient allocation rules for the multiarmed bandit problem with multiple plays-part I: I.i.d. rewards," IEEE Trans. Autom. Control, vol. 34, pp. 968-976, 1987a. (Pubitemid 18521625)
3. V. Anantharam, P. Varaiya, and J. Warland, "Asymptotically efficient allocation rules for the multiarmed bandit problem with multiple playspart II: Markovian rewards," IEEE Trans. Autom. Control, vol. 34, pp. 977-982, 1987b. (Pubitemid 18521626)
4. D. A. Berry and B. Fristedt, Bandit Problems. London, U.K.: Chapman and Hall, 1985.
5. M. K. Clayton, "Covariate models for bernoulli bandits," Sequential Anal., vol. 8, pp. 405-426, 1989.
6. J. C. Gittins, "Multiarmed Bandit Allocation Indices," in Wiley-Interscience Series in Systems and Optimization. Chichester, U.K.:Wiley, 1989.
7. A. Goldenshluger and A. Zeevi, "Woodroofe's one armed bandit problem revisited," Ann. Appl. Probab., vol. 19, pp. 1603-1633, 2009.
8. S. Kulkarni and G. Lugosi, "Finite time lower bounds for the two-armed bandit problem," IEEE Trans. Autom. Control, vol. 45, pp. 711-714, 2000.
9. T. L. Lai and H. Robbins, "Asymptotically optimal allocation of treatments in sequential experiments," in Design of Experiments. New York: Dekker, 1984, pp. 127-142.
10. T. L. Lai and H. Robbins, "Asymptotically efficient allocation rules," Adv. Appl. Math., vol. 6, pp. 4-22, 1985.
11. T. L. Lai, "Adaptive treatment allocation and the multiarmed bandit problem," Ann. Statist., vol. 15, pp. 1091-1114, 1987.
12. T. L. Lai and S.Yakowitz, "Machine learning and nonparametric bandit theory," IEEE Trans. Autom. Control, vol. 40, no. 7, pp. 1199-1209, Jul. 1995.
13. J. Langford and T. Zhang, , J. C. Platt, D. Koller, Y. Singer, and S. Roweis, Eds., "The epoch-greedy algorithm for multiarmed bandits with side information," in Advances in Neural Information Processing Systems. Cambridge, MA: MIT Press, 2008, vol. 20, pp. 817-824.
14. H. Robbins, "Some aspects of the sequential design of experiments," Bull. Amer. Math. Soc., vol. 55, pp. 527-535, 1952.
15. J. Sarkar, "One-armed bandit problems with covariates," Ann. Statist., vol. 19, pp. 1978-2002, 1991.
16. A. Tsybakov, Introduction to Nonparametric Estimation. New York: Springer, 2009.
17. C.-C. Wang, S. Kulkarni, and V. H. Poor, "Bandit problems with side observations," IEEE Trans. Autom. Control, vol. 50, no. 3, pp. 338-355, Mar. 2005. (Pubitemid 40448585)
18. M.Woodroofe, "A one-armed bandit problem with a concomitant variable," J. Amer. Statist. Assoc., vol. 74, pp. 799-806, 1979.
19. M. Woodroofe, "Sequential allocation with covariates," Sankhya Ser., vol. 44, pp. 403-414, 1982.
20. Y. Yang and D. Zhu, "Randomized allocation with nonparametric estimation for a multiarmed bandit problem with covariates," Ann. Statis., vol. 30, pp. 100-121, 2002. (Pubitemid 37095370)