Trading regret for efficiency: Online convex optimization with long term constraints

Journal of Machine Learning Research

Volumn 13, Issue , 2012, Pages 2503-2528

  Mahdavi, Mehrdad ^a   Jin, Rong ^a   Yang, Tianbao ^a  

^a Michigan State University   (United States)

Author keywords

Bandit feedback; Convex concave optimization; Online convex optimization; Variational inequality

Indexed keywords

COMPUTATIONAL CHALLENGES; CONVEX OPTIMIZATION PROBLEMS; CONVEX SET; EUCLIDEAN; FEEDBACK ALGORITHMS; FINITE NUMBER; LINEAR CONSTRAINTS; MULTIPOINT; OPTIMIZATION PROBLEMS; PROX-METHOD; VARIATIONAL INEQUALITIES; VIOLATION OF CONSTRAINTS;

ALGORITHMS; OPTIMIZATION; SET THEORY; VARIATIONAL TECHNIQUES;

CONVEX OPTIMIZATION;

EID: 84869152925     PISSN: 15324435     EISSN: 15337928     Source Type: Journal    
DOI: None     Document Type: Article

References (24)

1. Jacob Abernethy, Elad Hazan, and Alexander Rakhlin. Competing in the dark: An efficient algorithm for bandit linear optimization. In COLT, pages 263-274, 2008.
2. Jacob Abernethy, Alekh Agarwal, Peter L. Bartlett, and Alexander Rakhlin. A stochastic view of optimal regret through minimax duality. In COLT, 2009.
3. Jacob Abernethy, Elad Hazan, and Alexander Rakhlin. Interior-point methods for full-information and bandit online learning. IEEE Transactions on Information Theory, 58(7):4164-4175, 2012.
4. Alekh Agarwal, Ofer Dekel, and Lin Xiao. Optimal algorithms for online convex optimization with multi-point bandit feedback. In COLT, pages 28-40, 2010.
5. Baruch Awerbuch and Robert D. Kleinberg. Adaptive routing with end-to-end feedback: distributed learning and geometric approaches. In STOC, pages 45-53, 2004.
6. Peter L. Bartlett, Elad Hazan, and Alexander Rakhlin. Adaptive online gradient descent. In NIPS, pages 257-269, 2007.
7. Andrey Bernstein, Shie Mannor, and Nahum Shimkin. Online classification with specificity constraints. In NIPS, pages 190-198, 2010.
8. Dimitri P. Bertsekas, Angelia Nedic, and Asuman E. Ozdaglar. Convex Analysis and Optimization. Athena Scientific, 2003.
9. Stephen Boyd and Lieven Vandenberghe. Convex Optimization. Cambridge University Press, 2004.
10. Nicolo Cesa-Bianchi and Gabor Lugosi. Prediction, Learning, and Games. Cambridge University Press, 2006.
11. Nicolò Cesa-Bianchi, Alex Conconi, and Claudio Gentile. On the generalization ability of on-line learning algorithms. IEEE Transactions on Information Theory, 50(9):2050-2057, 2004.
12. Varsha Dani, Thomas P. Hayes, and Sham Kakade. The price of bandit information for online optimization. In NIPS, 2007.
13. John Duchi, Shai Shalev-Shwartz, Yoram Singer, and Tushar Chandra. Efficient projections onto the l1-ball for learning in high dimensions. In ICML, pages 272-279, 2008.
14. Abraham Flaxman, Adam Tauman Kalai, and H. Brendan McMahan. Online convex optimization in the bandit setting: gradient descent without a gradient. In SODA, pages 385-394, 2005. (Pubitemid 40851394)
15. Elad Hazan, Amit Agarwal, and Satyen Kale. Logarithmic regret algorithms for online convex optimization. Machine Learning, 69(2-3):169-192, 2007. (Pubitemid 47574314)
16. Jun Liu and Jieping Ye. Efficient euclidean projections in linear time. In ICML, pages 83-90, 2009.
17. Shie Mannor and John N. Tsitsiklis. Online learning with constraints. In COLT, pages 529-543, 2006. (Pubitemid 44072217)
18. Shie Mannor, John N. Tsitsiklis, and Jia Yuan Yu. Online learning with sample path constraints. Journal of Machine Learning Research, 10:569-590, 2009.
19. Hariharan Narayanan and Alexander Rakhlin. Random walk approach to regret minimization. In NIPS, pages 1777-1785, 2010.
20. Arkadi Nemirovski. Efficient methods in convex programming. Lecture Notes, Available at http://www2.isye.gatech.edu/nemirovs, 1994.
21. Arkadi Nemirovski. Prox-method with rate of convergence o(1/t) for variational inequalities with lipschitz continuous monotone operators and smooth convex-concave saddle point problems. SIAM J. on Optimization, 15(1):229-251, 2005. (Pubitemid 40360669)
22. Alexander Rakhlin. Lecture notes on online learning. Lecture Notes, Available at http://wwwstat. wharton.upenn.edu/rakhlin/papers, 2009.
23. Shai Shalev-Shwartz and Sham M. Kakade. Mind the duality gap: Logarithmic regret algorithms for online optimization. In NIPS, pages 1457-1464, 2008.
24. Martin Zinkevich. Online convex programming and generalized infinitesimal gradient ascent. In ICML, pages 928-936, 2003.