A penalized bandit algorithm

Electronic Journal of Probability

Volumn 13, Issue , 2008, Pages 341-373

  Lamberton, Damien ^a   Pagès, Gilles ^b  

^a UFR des Sciences et Technologie   (France)

^b SORBONNE UNIVERSITÉ   (France)

Author keywords

Convergence rate; Learning automata; Penalization; Stochastic approximation; Two armed bandit algorithm

Indexed keywords

EID: 41849113048     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v13-489     Document Type: Article

References (23)

1. Z.-D. BAI, F. HU (2005), ASYMPTOTICS IN RANDOMIZED URN MODELS, Annals of Applied Probability, 15, 914-940.
2. M. BENAIM (1999), DYNAMICS OF STOCHASTIC APPROXIMATION ALGORITHMS, Séminaire de Proba-bilités XXXIII, J. Azema, M. Emery, M. Ledoux, M. Yor eds., Lecture Notes in Mathematics n01709, pp.1-68.
3. C. BOUTON (1988), APPROXIMATION GAUSSIENNE D'ALGORITHMES STOCHASTIQUES A DYNAMIQUE MARKOVIENNE, Ann. Inst. Henri Poincaré, Probab. Stat., 24(1), 131-155.
4. L. DUBINS AND D. FREEDMAN (1965), A SHARPER FORM OF THE BOREL-CANTELLI LEMMA AND THE STRONG LAW, Ann. Of Math. Stat., 36, 800-807.
5. D. DUFFIE, J. PAN, K. SINGLETON (2000), TRANSFORM ANALYSIS AND ASSET PRICING FOR AFFINE JUMP-DIFFUSIONS, Econometrica, 68, 1343-1376.
6. D. DUFFIE, D. FILIPOVIC, W. SCHACHERMAYER (2003), AFFINE PROCESSES AND APPLICATIONS IN FINANCE. Ann. Appl. Probab., 13(3), 984-1053
7. M. DUFLO (1996), ALGORITHMES STOCHASTIQUES, COLL. Mathématiques & Applications, 23, Springer-Verlag, Berlin, 319p.
8. J. JACOD, A.N. SHIRYAEV (2003), LIMIT THEOREMS FOR STOCHASTIC PROCESSES, 2nd edition, Fundamental Principles of Mathematical Sciences, 28, Springer-Verlag, Berlin, 661p.
9. S. KARLIN, H.M. TAYLOR (1981), A second course in stochastic processes, Academic Press, New-York.
10. H.J. KUSHNER, D.S. CLARK (1978), STOCHASTIC APPROXIMATION FOR CONSTRAINED AND UNCONSTRAINED SYSTEMS, Applied Math. Science Series, 26, Springer-Verlag, New York.
11. H.J. KUSHNER, G.G. YIN (2003), STOCHASTIC APPROXIMATION AND RECURSIVE ALGORITHMS AND APPLICATIONS, 2nd edition, Applications of Mathematics, Stochastic Modelling and Applied Probability, 35, Springer-Verlag, New York.
12. S. LAKSHMIVARAHAN (1979), E-OPTIMAL LEARNING ALGORITHMS-NON-ABSORBING BARRIER TYPE, UNIV. OKLAHOMA, SCHOOL OF ELECTRICAL ENGINEERING AND COMPUTING SCIENCE, TECHN. REPORT EECS 7901.
13. S. LAKSHMIVARAHAN (1981), Learning Algotithms: Theory and Applications, New York, Springer-verlag.
14. D. LAMBERTON, G. PAGES (2005), HOW FAST IS THE BANDIT?, PRE-PRINT LPMA-1018, UNIV. PARIS 6, FORTHCOMING IN Stochastic Analysis and Applications.
15. D. LAMBERTON, G. PAGES, P. TARRES (2004), WHEN CAN THE TWO-ARMED BANDIT ALGORITHM BE TRUSTED?, Annals of Applied Probability, 14(3), 1424-1454.
16. P. MASSART (2003), St-Flour Lecture Notes, Cours de l'école d'été de Saint-Flour 2003, pre-print, Univ. Paris-Sud (France), http://www.math.u-psud.fr/massart/flour.pdf.
17. K.S. NARENDRA, M.A.L. THATHACHAR (1974), Learning Automata - A survey, IEEE Trans. Systems, Man., Cybernetics, S.M.C-4, 323-334.
18. K.S. NARENDRA, M.A.L. THATHACHAR (1989), Learning Automata - An introduction, Prentice Hall, Englewood Cliffs, NJ, 476p.
19. M.F. NORMAN (1968), On linear Models with Two Absorbing Barriers, J. Of Mathematical Psychlogy, 5, 225-241.
20. R. PEMANTLE (1990), Non-convergence to unstable points in urn models and stochastic approximations, Annals of Probability, 18, n0 2, 698-712.
21. I.J. SHAPIRO, K.S. NARENDRA (1969), Use of Stochastic Automata for Parameter SelfOptimization with Multi-Modal Perfomance Criteria, IEEE Trans. Syst. Sci. And Cybern., SSC-5, 352-360.
22. P. TARRES, Algorithmes stochastiques et marches aléatoires renforcées, These de l'ENS Cachan (France), novembre 2001.
23. P. Tarr's, P. Vandekerkhove, On the ergodic two armed-bandit algorithm, preprint, 2006.