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Strategies for prediction under imperfect monitoring

Author

Listed:
  • Gabor Lugosi

    (ICREA - Institució Catalana de Recerca i Estudis Avançats = Catalan Institution for Research and Advanced Studies)

  • Shie Mannor

    (McGill University = Université McGill [Montréal, Canada])

  • Gilles Stoltz

    (DMA - Département de Mathématiques et Applications - ENS Paris - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique, GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique)

Abstract

We propose simple randomized strategies for sequential prediction under imperfect monitoring, that is, when the forecaster does not have access to the past outcomes but rather to a feedback signal. The proposed strategies are consistent in the sense that they achieve, asymptotically, the best possible average reward. It was Rustichini (1999) who first proved the existence of such consistent predictors. The forecasters presented here offer the first constructive proof of consistency. Moreover, the proposed algorithms are computationally efficient. We also establish upper bounds for the rates of convergence. In the case of deterministic feedback, these rates are optimal up to logarithmic terms.

Suggested Citation

  • Gabor Lugosi & Shie Mannor & Gilles Stoltz, 2008. "Strategies for prediction under imperfect monitoring," Post-Print hal-00124679, HAL.
    • Handle: RePEc:hal:journl:hal-00124679
    Note: View the original document on HAL open archive server: https://hal.science/hal-00124679v4
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    References listed on IDEAS

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    1. MERTENS , Jean-François & SORIN , Sylvain & ZAMIR , Shmuel, 1994. "Repeated Games. Part B : The Central Results," LIDAM Discussion Papers CORE 1994021, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Nicolò Cesa-Bianchi & Gábor Lugosi & Gilles Stoltz, 2006. "Regret Minimization Under Partial Monitoring," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 562-580, August.
    3. Sergiu Hart & Andreu Mas-Colell, 2013. "A Simple Adaptive Procedure Leading To Correlated Equilibrium," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 2, pages 17-46, World Scientific Publishing Co. Pte. Ltd..
    4. MERTENS , Jean-François & SORIN , Sylvain & ZAMIR , Shmuel, 1994. "Repeated Games. Part A : Background Material," LIDAM Discussion Papers CORE 1994020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Chen, Xiaohong & White, Halbert, 1996. "Laws of Large Numbers for Hilbert Space-Valued Mixingales with Applications," Econometric Theory, Cambridge University Press, vol. 12(2), pages 284-304, June.
    6. Nicolo Cesa Bianchi & Gábor Lugosi, 1998. "On prediction of individual sequences," Economics Working Papers 324, Department of Economics and Business, Universitat Pompeu Fabra.
    7. Rustichini, Aldo, 1999. "Minimizing Regret: The General Case," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 224-243, October.
    8. Nimrod Megiddo, 1979. "On Repeated Games with Incomplete Information Played by Non-Bayesian Players," Discussion Papers 373, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    9. Sergiu Hart & Andreu Mas-Colell, 2013. "A Reinforcement Procedure Leading To Correlated Equilibrium," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 4, pages 77-98, World Scientific Publishing Co. Pte. Ltd..
    10. MERTENS, Jean-François & SORIN , Sylvain & ZAMIR , Shmuel, 1994. "Repeated Games. Part C : Further Developments," LIDAM Discussion Papers CORE 1994022, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Vianney Perchet & Marc Quincampoix, 2015. "On a Unified Framework for Approachability with Full or Partial Monitoring," Mathematics of Operations Research, INFORMS, vol. 40(3), pages 596-610, March.
    2. Ehud Lehrer & Eilon Solan, 2007. "Learning to play partially-specified equilibrium," Levine's Working Paper Archive 122247000000001436, David K. Levine.
    3. Ehud Lehrer & Eilon Solan, 2016. "A General Internal Regret-Free Strategy," Dynamic Games and Applications, Springer, vol. 6(1), pages 112-138, March.
    4. Gábor Bartók & Dean P. Foster & Dávid Pál & Alexander Rakhlin & Csaba Szepesvári, 2014. "Partial Monitoring---Classification, Regret Bounds, and Algorithms," Mathematics of Operations Research, INFORMS, vol. 39(4), pages 967-997, November.

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