Hannan Consistency in On-Line Learning in Case of Unbounded Losses Under Partial Monitoring

Authors: Chamy Allenberg, Peter Auer, László Györfi, and György Ottucsák

Source: Algorithmic Learning Theory, 17th International Conference, ALT 2006, Barcelona, October 2006, Proceedings, (José L. Balcázar, Phil Long and Frank Stephan, Eds.), Lecture Notes in Artificial Intelligence 4264, pp. 229 - 243, Springer 2006.

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 &epsilon ≤ 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.

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