Potential-based algorithms in on-line prediction and game theory

Machine Learning

Volumn 51, Issue 3, 2003, Pages 239-261

  Cesa Bianchi, Nicolò ^a   Lugosi, Gábor ^b  

^a UNIVERSITY OF MILAN   (Italy)

^b UNIVERSITAT POMPEU FABRA   (Spain)

Author keywords

Blackwell's strategy; Boosting; Internal regret; On line learning; Perceptron algorithm; Universal prediction; Weighted average predictors

Indexed keywords

DECISION THEORY; GAME THEORY; LEARNING SYSTEMS; MATHEMATICAL MODELS; PROBABILITY; THEOREM PROVING; VECTORS;

BLACKWELL STRATEGY; BOOSTING; INTERNAL REGRET; ON-LINE PREDICTION; PERCEPTRON ALGORITHM; POTENTIAL-BASED ALGORITHMS; UNIVERSAL PREDICTION; WEIGHTED AVERAGE PREDICTORS;

ALGORITHMS;

EID: 0037614825     PISSN: 08856125     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022901500417     Document Type: Article

References (38)

1. Auer, P., Cesa-Bianchi, N., & Gentile, C. (2002). Adaptive and self-confident on-line learning algorithms. Journal of Computer and System Sciences, 64: 1, 48-75.
2. Blackwell, D. (1956). An analog of the minimax theorem for vector payoffs. Pacific Journal of Mathematics, 6, 1-8.
3. Block, H. (1962). The perceptron: A model for brain functioning. Review of Modern Physics, 34, 123-135.
4. Bregman, L. (1967). The relaxation method of finding the common point of convex sets and its application to the solutions of problems in convex programming. USSR Computational Mathematics and Physics, 7, 200-217.
5. Cesa-Bianchi, N. (1999). Analysis of two gradient-based algorithms for on-line regression. Journal of Computer and System Sciences, 59:3, 392-411.
6. Cesa-Bianchi, N., Freund, Y., Helmbold, D., Haussler, D., Schapire, R., & Warmuth, M. (1997). How to use expert advice. Journal of the ACM, 44:3, 427-485.
7. Cesa-Bianchi, N., Conconi, A., & Gentile, C. (2002). A second-order perceptron algorithm. In Proceedings of the 15th Annual Conference on Computational Learning Theory, Lecture Notes in Artificial Intelligence, Springer, 2002.
8. Cohen, W., & Singer, Y. (1999). Context-sensitive learning methods for text categorization. ACM Transactions on Information Systems, 17:2, 141-173.
9. Cover, T., & Thomas, J. (1991). Elements of Information Theory. John Wiley and Sons.
10. Foster, D., & Vohra, R. (1997). Calibrated learning and correlated equilibrium. Games and Economic Behaviour, 21, 40-55.
11. Foster, D., & Vohra, R. (1999). Regret in the on-line decision problem. Games and Economic Behavior, 29:1/2, 7-35.
12. Freund, Y., & Schapire, R. (1997). A decision-theoretic generalization of on-line learning and an application to boosting. Journal of Computer and System Sciences,55:1, 119-139.
13. Freund, Y., & Schapire, R. (1999a). Adaptive game playing using multiplicative weights. Games and Economic Behavior, 29, 79-103.
14. Freund, Y., & Schapire, R. (1999b). Large margin classification using the perceptron algorithm. Machine Learning, 37:3, 277-296.
15. Freund, Y., Schapire, R., Singer, Y., & Warmuth, M. (1997). Using and combining predictors that specialize. In Proceedings of the 29th Annual ACM Symposium on the Theory of Computing (pp. 334-343). ACM Press.
16. Fudenberg, D., & Levine, D. (1995). Universal consistency and cautious fictitious play. Journal of Economic, Dynamics, and Control, 19, 1065-1090.
17. Fudenberg, D., & Levine, D. (1999). Conditional universal consistency. Games and Economic Behaviour, 29, 7-35.
18. Gentile, C. (2001). The robustness of the p-norm algorithms. An extended abstract (co-authored with N. Littlestone) appeared in the Proceedings of the 12th Annual Conference on Computational Learning Theory (pp. 1-11). ACM Press, 1999.
19. Gentile, C., & Warmuth, M. (1999). Linear hinge loss and average margin. In Advances in Neural Information Processing Systems 10 MIT Press.
20. Grove, A., Littlestone, N., & Schuurmans, D. (1997). General convergence results for linear discriminant updates. In Proceedings of the 10th Annual Conference on Computational Learning Theory (pp. 171-183). ACM Press.
21. Grove, A., Littlestone, N., & Schuurmans, D. (2001). General convergence results for linear discriminant updates. Machine Learning, 43:3, 173-210.
22. Hannan, J. (1957). Approximation to bayes risk in repeated play. Contributions to the Theory of Games, 3, 97-139.
23. Hart, S., & Mas-Colell, A. (2000). A simple adaptive procedure leading to correlated equilibrium. Econometrica, 68, 1127-1150.
24. Hart, S., & Mas-Colell, A. (2001). A general class of adaptive strategies. Journal of Economic Theory, 98:1, 26-54.
25. Haussler, D., Kivinen, J., & Warmuth, M. (1998). Sequential prediction of individual sequences under general loss functions. IEEE Transactions on Information Theory, 44, 1906-1925.
26. Kivinen, J., & Warmuth, M. (1999). Averaging expert predictions. Lecture Notes in Artificial Intelligence, (pp. 153-167). In Proceedings of the Fourth European Conference on Computational Learning Theory vol. 1572. Springer.
27. Kivinen, J., & Warmuth, M. (2001). Relative loss bounds for multidimensional regression problems. Machine Learning, 45:3, 301-329.
28. Lehrer, E. (2001). A wide range no-regret theorem. Games and Economic Behavior, in press.
29. Littlestone, N. (1989). Mistake bounds and logarithmic linear-threshold learning algorithms. Ph.D. Thesis, University of California at Santa Cruz.
30. Littlestone, N., & Warmuth, M. (1994). The weighted majority algorithm. Information and Computation, 108, 212-261.
31. Novikoff, A. (1962). On convergence proofs of perceptrons. In Proceedings of the Symposium on the Mathematical Theory of Automata, vol. XII, pp. 615-622.
32. Rosenblatt, F. (1962). Principles of Neurodynamics. Spartan Books.
33. Schapire, R. (2001). Drifting games. Machine Learning, 43:5, 265-291.
34. Seneta, E. (1981). Non-Negative Matrices and Markov Chains. Springer.
35. Vovk, V. (1990). Aggregating strategies. In Proceedings of the 3rd Annual Workshop on Computational Learning Theory. pp. 372-383.
36. Vovk, V. (1998). A game of prediction with expert advice. Journal of Computer and System Sciences, 56: 2, 153-173.
37. Vovk, V. (2001). Competitive on-line statistics. International Statistical Review, 69, 213-248.
38. Warmuth, M., & Jagota, A. (1997). Continuous and discrete-time nonlinear gradient descent: Relative loss bounds and convergence. In Electronic Proceedings of the 5th International Symposium on Artificial Intelligence and Mathematics.