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 [11] 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.
S. M. was partially supported by the Canada Research Chairs Program and by the Natural Sciences and Engineering Research Council of Canada. G.L. acknowledges the support of the Spanish Ministry of Science and Technology grant MTM2006-05650. G.S. was partially supported by the French “Agence Nationale pour la Recherche” under grant JCJC06-137444 “From applications to theory in learning and adaptive statistics.” G.L. and G.S. acknowledge the PASCAL Network of Excellence under EC grant no. 506778.
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Lugosi, G., Mannor, S., Stoltz, G. (2007). Strategies for Prediction Under Imperfect Monitoring. In: Bshouty, N.H., Gentile, C. (eds) Learning Theory. COLT 2007. Lecture Notes in Computer Science(), vol 4539. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72927-3_19
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DOI: https://doi.org/10.1007/978-3-540-72927-3_19
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