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arXiv: math/0701419

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Mathematics of Operations Research (2008) à paraître

Available versions:

v1 (2007-01-15)

v2 (2007-04-22)

v3 (2007-07-12)

v4 (2008-01-07)

Strategies for prediction under imperfect monitoring

Gabor Lugosi 1, Shie Mannor 2, Gilles Stoltz (  Corresponding author ) 3, 4

(2008)

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.

1:	Institució Catalana de Recerca i Estudis Avançats [Barcelona] (ICREA)
	ICREA – Universitat de Barcelona – Fundació Catalana per a la Recerca i la Innovació (FCRI)
2:	McGill University (McGill)
	McGill University
3:	Département de Mathématiques et Applications (DMA)
	CNRS : UMR8553 – Ecole Normale Supérieure de Paris - ENS Paris
4:	Groupement de Recherche et d'Etudes en Gestion à HEC (GREGH)
	GROUPE HEC – CNRS : UMR2959

Subject

:

Mathematics/Statistics Statistics/Statistics Theory Computer Science/Learning Humanities and Social Sciences/Economies and finances

Keyword(s): individual sequences – repeated games with partial monitoring – approachability

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From: Gilles Stoltz <>

Submitted on: Monday, 7 January 2008 15:03:46

Updated on: Monday, 28 January 2008 23:22:09