Following the leader and fast rates in linear prediction: Curved constraint sets and other regularities

Advances in Neural Information Processing Systems

Volumn , Issue , 2016, Pages 4976-4984

  Huang, Ruitong ^a   Lattimore, Tor ^b   Gyørgy, András ^c   Szepesvári, Csaba ^a  

^a UNIVERSITY OF ALBERTA   (Canada)

^b INDIANA UNIVERSITY   (United States)

^c IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

FOLLOW THE LEADERS; LINEAR PREDICTION; LOGARITHMIC GROWTH; LOSS FUNCTIONS; META-ALGORITHMS; ONLINE LEARNING ALGORITHMS; POLYHEDRAL DOMAINS; STOCHASTIC DATA;

STOCHASTIC SYSTEMS;

EID: 85018878433     PISSN: 10495258     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (24)

1. Y. Abbasi-Yadkori. Forced-exploration based algorithms for playing in bandits with large action sets. Library and Archives Canada, 2010.
2. J. Abernethy, P.L. Bartlett, A. Rakhlin, and A. Tewari. Optimal strategies and minimax lower bounds for online convex games. In 21st Annual Conference on Learning Theory (COLT), 2008.
3. P.L. Bartlett, E. Hazan, and A. Rakhlin. Adaptive online gradient descent. In Advances in Neural Information Processing Systems (NIPS), pages 65-72, 2007.
4. D. Bertsekas. Nonlinear Programming. Athena Scientific, Belmont, MA, 1999.
5. N. Cesa-Bianchi and G. Lugosi. Prediction, Learning, and Games. Cambridge University Press, New York, NY, USA, 2006.
6. N. Cesa-Bianchi, A. Conconi, and C. Gentile. On the generalization ability of on-line learning algorithms. IEEE Trans. Information Theory, 50(9):2050-2057, 2004.
7. D.J. Foster, A. Rakhlin, and K. Sridharan. Adaptive online learning. In Advances in Neural Information Processing Systems (NIPS), pages 3357-3365, 2015.
8. Y. Freund and R. Schapire. A decision-theoretic generalization of on-line learning and an application to boosting. Journal of Computer and System Sciences, 55:119-139, 1997.
9. A.A. Gaivoronski and F. Stella. Stochastic nonstationary optimization for finding universal portfolios. Annals of Operations Research, 100(1-4):165-188, 2000.
10. D. Garber and E. Hazan. Faster rates for the frank-wolfe method over strongly-convex sets. In Proceedings of the 32nd International Conference on Machine Learning (ICML), Volume 951, pages 541-549, 2015.
11. E. Hazan, A. Agarwal, and S. Kale. Logarithmic regret algorithms for online convex optimization. Machine Learning, 69(2-3):169-192, 2007.
12. R. Huang, T. Lattimore, A. Gyørgy, and Cs Szepesvári. Following the leader and fast rates in linear prediction: Curved constraint sets and other regularities. arXiv, 2016.
13. S. M. Kakade and S. Shalev-Shwartz. Mind the duality gap: Logarithmic regret algorithms for online optimization. In Advances in Neural Information Processing Systems (NIPS), pages 1457-1464, 2009.
14. W. Kotłowski. Minimax strategy for prediction with expert advice under stochastic assumptions. Algorithmic Learning Theory (ALT), 2016.
15. E.S. Levitin and B.T. Polyak. Constrained minimization methods. USSR Computational Mathematics and Mathematical Physics, 6(5):1-50, 1966.
16. H.B. McMahan. Follow-the-regularized-leader and mirror descent: Equivalence theorems and implicit updates. arXiv, 2010. URL http://arxiv.org/abs/1009.3240.
17. N. Merhav and M. Feder. Universal sequential learning and decision from individual data sequences. In 5th Annual ACM Workshop on Computational Learning Theory (COLT), pages 413-427. ACM Press, 1992.
18. F. Orabona, N. Cesa-Bianchi, and C. Gentile. Beyond logarithmic bounds in online learning. In Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics (AISTATS), pages 823-831, 2012.
19. A. Rakhlin and K. Sridharan. Online learning with predictable sequences. In 26th Annual Conference on Learning Theory (COLT), pages 993-1019, 2013.
20. A. Sani, G. Neu, and A. Lazaric. Exploiting easy data in online optimization. In Advances in Neural Information Processing Systems (NIPS), pages 810-818, 2014.
21. R. Schneider. Convex Bodies: The Brunn-Minkowski Theory. Encyclopedia of Mathematics and its Applications. Cambridge Univ. Press, 2nd edition, 2014.
22. S. Shalev-Shwartz. Online learning and online convex optimization. Foundations and trends in Machine Learning, 4(2):107-194, 2012.
23. S. Shalev-Shwartz and S. Ben-David. Understanding Machine Learning: From Theory to Algorithms. Cambridge University Press, New York, NY, USA, 2014.
24. T. van Erven, P. Grünwald, N. Mehta, M. Reid, and R. Williamson. Fast rates in statistical and online learning. Journal of Machine Learning Research (JMLR), 16:1793-1861, 2015. Special issue in Memory of Alexey Chervonenkis.