Lipschitz bandits without the Lipschitz constant

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 6925 LNAI, Issue , 2011, Pages 144-158

  Bubeck, Sébastien ^a   Stoltz, Gilles ^b,c   Yu, Jia Yuan ^b,c  

^a CENTRE DE RECERCA MATEMÀTICA   (Spain)

^b ECOLE NORMALE SUPÉRIEURE   (France)

^c HEC PARIS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

BANDIT PROBLEMS; LIPSCHITZ; LIPSCHITZ CONSTANT; MINIMAX; ORDERS OF MAGNITUDE; PERFORMANCE GUARANTEES; TIME INSTANCES; TUNING PARAMETER;

ALGORITHMS;

EID: 80054092590     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-24412-4_14     Document Type: Conference Paper

References (18)

1. Audibert, J.-Y., Bubeck, S.: Regret bounds and minimax policies under partial monitoring. Journal of Machine Learning Research 11, 2635-2686 (2010)
2. Audibert, J.-Y., Bubeck, S., Lugosi, G.: Minimax policies for combinatorial prediction games. In: Proceedings of the 24th Annual Conference on Learning Theory. Omnipress (2011)
3. Auer, P., Cesa-Bianchi, N., Fischer, P.: Finite-time analysis of the multiarmed bandit problem. Machine Learning Journal 47(2-3), 235-256 (2002)
4. Auer, P., Cesa-Bianchi, N., Freund, Y., Schapire, R.: The non-stochastic multi-armed bandit problem. SIAM Journal on Computing 32(1), 48-77 (2002)
5. Agrawal, R.: The continuum-armed bandit problem. SIAM Journal on Control and Optimization 33, 1926-1951 (1995)
6. Auer, P., Ortner, R., Szepesvári, C.: Improved rates for the stochastic continuum-armed bandit problem. In: Bshouty, N.H., Gentile, C. (eds.) COLT. LNCS (LNAI), vol. 4539, pp. 454-468. Springer, Heidelberg (2007)
7. Bubeck, S., Munos, R.: Open-loop optimistic planning. In: Proceedings of the 23rd Annual Conference on Learning Theory. Omnipress (2010)
8. Bubeck, S., Munos, R., Stoltz, G., Szepesvári, C.: X-armed bandits. Journal of Machine Learning Research 12, 1655-1695 (2011)
9. Bubeck, S., Stoltz, G., Yu, J.Y.: Lipschitz bandits without the lipschitz constant (2011), http://arxiv.org/pdf/1105.5041
10. Cope, E.: Regret and convergence bounds for immediate-reward reinforcement learning with continuous action spaces. IEEE Transactions on Automatic Control 54(6), 1243-1253 (2009)
11. Dani, V., Hayes, T.P., Kakade, S.M.: Stochastic linear optimization under bandit feedback. In: Proceedings of the 21st Annual Conference on Learning Theory, pp. 355-366. Omnipress (2008)
12. Horn, M.: Optimal algorithms for global optimization in case of unknown Lipschitz constant. Journal of Complexity 22(1) (2006)
13. Jones, D.R., Perttunen, C.D., Stuckman, B.E.: Lipschitzian optimization without the Lipschitz constant. Journal of Optimization Theory and Applications 79(1), 157-181 (1993)
14. Kleinberg, R.: Nearly tight bounds for the continuum-armed bandit problem. In: Advances in Neural Information Processing Systems, pp. 697-704 (2004)
15. Kleinberg, R., Slivkins, A., Upfal, E.: Multi-armed bandits in metric spaces. In: Proceedings of the 40th ACM Symposium on Theory of Computing (2008)
16. Robbins, H.: Some aspects of the sequential design of experiments. Bulletin of the American Mathematics Society 58, 527-535 (1952)
17. Wang, Y., Audibert, J.Y., Munos, R.: Algorithms for infinitely manyarmed bandits. In: Advances in Neural Information Processing Systems, pp. 1729-1736 (2009)
18. Yu, J.Y., Mannor, S.: Unimodal bandits. In: Proceedings of the 28th International Conference on Machine Learning (2011)