Minimizing regret with label-efficient prediction

Nicolo Cesa-Bianchi (1) , Gabor Lugosi (2) , Gilles Stoltz (3)

1 Dipartimento di Scienze dell'Informazione [Milano]
2 Department of Economics
3 DMA - Département de Mathématiques et Applications - ENS Paris

We investigate label efficient prediction, a variant, proposed by Helmbold and Panizza, of the problem of prediction with expert advice. In this variant the forecaster, after guessing the next element of the sequence to be predicted, does not observe its true value unless he asks for it, which he cannot do too often. We determine matching upper and lower bounds for the best possible excess prediction error, with respect to the best possible constant predictor, when the number of allowed queries is fixed. We also prove that Hannan consistency, a fundamental property in game-theoretic prediction models, can be achieved by a forecaster issuing a number of queries growing to infinity at a rate just slightly faster than logarithmic in the number of prediction rounds.

Keywords: individual sequences; label efficient prediction; on-line learning; prediction with expert advice

Domains: Statistics [math.ST]

Nicolo Cesa-Bianchi, Gabor Lugosi, Gilles Stoltz. Minimizing regret with label-efficient prediction. IEEE Transactions on Information Theory, 2005, 51, pp.2152-2162. ⟨hal-00007537⟩