Abstract
In this paper the sequential prediction problem with expert advice is considered when the loss is unbounded under partial monitoring scenarios. We deal with a wide class of the partial monitoring problems: the combination of the label efficient and multi-armed bandit problem, that is, where the algorithm is only informed about the performance of the chosen expert with probability ε≤1. For bounded losses an algorithm is given whose expected regret scales with the square root of the loss of the best expert. For unbounded losses we prove that Hannan consistency can be achieved, depending on the growth rate of the average squared losses of the experts.
We would like to thank Gilles Stoltz and András György for useful comments.
This research was supported in part by the Hungarian Inter-University Center for Telecommunications and Informatics (ETIK).
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Allenberg, C., Auer, P., Györfi, L., Ottucsák, G. (2006). Hannan Consistency in On-Line Learning in Case of Unbounded Losses Under Partial Monitoring . In: Balcázar, J.L., Long, P.M., Stephan, F. (eds) Algorithmic Learning Theory. ALT 2006. Lecture Notes in Computer Science(), vol 4264. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11894841_20
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DOI: https://doi.org/10.1007/11894841_20
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