Beating the adaptive bandit with high probability

COLT 2009 - The 22nd Conference on Learning Theory

Volumn , Issue , 2009, Pages

  Abernethy, Jacob ^a   Rakhlin, Alexander ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ADAPTIVE ADVERSARY; BANDIT PROBLEMS; CONFIDENCE INTERVAL; HIGH PROBABILITY; LOWER BOUNDS; MISSING INFORMATION; SAMPLING SCHEMES; SELF-CONCORDANT BARRIERS;

ALGORITHMS;

PROBABILITY;

EID: 84898073179     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (17)

1. J. Abernethy, E. Hazan, and A. Rakhlin. Competing in the dark: An efficient algorithm for bandit linear optimization. In Proceedings of The Twenty First Annual Conference on Learning Theory, 2008.
2. J. Abernethy and A. Rakhlin. Beating the adaptive bandit with high probability. Technical Report UCB/EECS-2009-10, EECS Department, University of California, Berkeley, Jan 2009.
3. Peter Auer, Nicolò Cesa-Bianchi, Yoav Freund, and Robert E. Schapire. The nonstochastic multiarmed bandit problem. SIAM J. Comput., 32(1): 48-77, 2003.
4. Baruch Awerbuch and Robert D. Kleinberg. Adaptive routing with end-to-end feedback: distributed learning and geometric approaches. In STOC'04, pages 45-53, New York, NY, USA, 2004. ACM.
5. P. L. Bartlett, V. Dani, T. Hayes, S. Kakade, A. Rakhlin, and A. Tewari. High probability regret bounds for online optimization. In Proceedings of The Twenty First Annual Conference on Learning Theory, 2008.
6. Amir Beck and Marc Teboulle. Mirror descent and nonlinear projected subgradient methods for convex optimization. Oper. Res. Lett., 31(3): 167-175, 2003.
7. Y. Censor and S. A. Zenios. Parallel Optimization: Theory, Algorithms, and Applications. Oxford University Press, 1997.
8. Nicolò Cesa-Bianchi and Gábor Lugosi. Prediction, Learning, and Games. Cambridge Univ. Press, 2006.
9. Varsha Dani, Thomas Hayes, and Sham Kakade. The price of bandit information for online optimization. In J.C. Platt, D. Koller, Y. Singer, and S. Roweis, editors, NIPS'08. MIT Press, Cambridge, MA, 2008.
10. Varsha Dani and Thomas P. Hayes. Robbing the bandit: less regret in online geometric optimization against an adaptive adversary. In SODA'06, pages 937-943, New York, NY, USA, 2006. ACM.
11. Abraham D. Flaxman, Adam Tauman Kalai, and H. Brendan McMahan. Online convex optimization in the bandit setting: gradient descent without a gradient. In SODA'05: Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms, pages 385-394, Philadelphia, PA, USA, 2005. Society for Industrial and Applied Mathematics.
12. A. György, T. Linder, G. Lugosi, and G. Ottucsák. The on-line shortest path problem under partial monitoring. JMLR, 8: 2369-2403, 2007.
13. H. Brendan McMahan and Avrim Blum. Online geometric optimization in the bandit setting against an adaptive adversary. In COLT, pages 109-123, 2004.
14. A. Nemirovski and M. Todd. Interior-point methods for optimization. Acta Numerica, pages 191-234, 2008.
15. Y. E. Nesterov and A.S. Nemirovskii. Interior Point Polynomial Algorithms in Convex Programming. SIAM, Philadelphia, 1994.
16. A. Rakhlin and A. Tewari. Lecture notes on online learning, 2008. Available at http://www-stat.wharton.upenn.edu/~rakhlin/papers/online-learning. pdf.
17. Shai Shalev-Shwartz. Online Learning: Theory, Algorithms, and Applications. PhD thesis, Hebrew University, 2007.