Bandit Theory meets Compressed Sensing for high-dimensional Stochastic Linear Bandit

Journal of Machine Learning Research

Volumn 22, Issue , 2012, Pages 190-198

  Carpentier, Alexandra ^a   Munos, Remi ^a  

^a INRIA   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE; BUDGET CONTROL; SIGNAL RECONSTRUCTION; STOCHASTIC SYSTEMS;

BANDIT PROBLEMS; BANDIT THEORIES; HIGH-DIMENSIONAL; REGRET BOUNDS; UNIT BALL;

COMPRESSED SENSING;

EID: 84896062989     PISSN: 15324435     EISSN: 15337928     Source Type: Journal    
DOI: None     Document Type: Conference Paper

References (19)

1. E. Moulines, A. Garivier. On upper-confidence bound policies for non-stationary bandit problems. In Algorithmic Learning Theory (ALT), 2011.
2. Y. Abbasi-yadkori, D. Pal, and C. Szepesvari. Improved algorithms for linear stochastic bandits. In Advances in Neural Information Processing Systems, 2011.
3. Y. Abbasi-yadkori, D. Pal, and C. Szepesvari. Online-to-confidence-set conversions and application to sparse stochastic bandits. In Artificial Intelligence and Statistics, 2012.
4. J. Abernethy, E. Hazan, and A. Rakhlin. Competing in the dark: An efficient algorithm for bandit linear optimization. In Proceedings of the 21st Annual Conference on Learning Theory (COLT), volume 3. Citeseer, 2008.
5. J.Y. Audibert, S. Bubeck, and G. Lugosi. Minimax policies for combinatorial prediction games. Arxiv pre-print arXiv:1105.4871, 2011.
6. P.L. Bartlett, V. Dani, T. Hayes, S.M. Kakade, A. Rakhlin, and A. Tewari. High-probability regret bounds for bandit online linear optimization. In Proceedings of the 21st Annual Conference on Learning Theory (COLT 2008), pages 335-342. Citeseer, 2008.
7. D. P. Bertsekas. Nonlinear programming. Athena Scientific Belmont, MA, 1999.
8. T. Blumensath and M.E. Davies. Iterative hard thresholding for compressed sensing. Applied and Computational Harmonic Analysis, 27(3):265-274, 2009.
9. E. Candes and T. Tao. The dantzig selector: statistical estimation when p is much larger than n. The Annals of Statistics, 35(6):2313-2351, 2007.
10. N. Cesa-Bianchi and G. Lugosi. Combinatorial bandits. In Proceedings of the 22nd Annual Conference on Learning Theory (COLT 09). Citeseer, 2009.
11. S.S. Chen, D.L. Donoho, and M.A. Saunders. Atomic decomposition by basis pursuit. SIAM journal on scientific computing, 20(1):33-61, 1999.
12. V. Dani, T.P. Hayes, and S.M. Kakade. Stochastic linear optimization under bandit feedback. In Proceedings of the 21st Annual Conference on Learning Theory (COLT). Citeseer, 2008.
13. S. Filippi, O. Cappe, A. Garivier, and C. Szepesvari. Parametric bandits: The generalized linear case. In Advances in Neural Information Processing Systems, 2010.
14. A.D. Flaxman, A.T. Kalai, and H.B. McMahan. Online convex optimization in the bandit setting: gradient descent without a gradient. In Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms, pages 385-394. Society for Industrial and Applied Mathematics, 2005.
15. W.M. Koolen, M.K. Warmuth, and J. Kivinen. Hedging structured concepts. In Proceedings of the 23rd Annual Conference on Learning Theory (COLT 19). Omnipress, 2010.
16. J. Nino-Mora. Restless bandits, partial conservation laws and indexability. Advances in Applied Probability, 33(1):76-98, 2001.
17. P. Rusmevichientong and J.N. Tsitsiklis. Linearly parameterized bandits. Arxiv preprint arXiv:0812.3465, 2008.
18. A. Slivkins and E. Upfal. Adapting to a changing environment: The brownian restless bandits. In Proc. 21st Annual Conference on Learning Theory, pages 343-354. Citeseer, 2008.
19. P. Whittle. Restless bandits: Activity allocation in a changing world. Journal of applied probability, pages 287-298, 1988.