A new look at shifting regret

Nicolò Cesa-Bianchi (1) , Pierre Gaillard (2, 3) , Gabor Lugosi (4, 5) , Gilles Stoltz (2, 3, 6)

1 Dipartimento di Scienze dell'Informazione [Milano]
2 CLASSIC - Computational Learning, Aggregation, Supervised Statistical, Inference, and Classification
3 DMA - Département de Mathématiques et Applications - ENS Paris
4 ICREA - Institució Catalana de Recerca i Estudis Avançats = Catalan Institution for Research and Advanced Studies
5 UPF - Universitat Pompeu Fabra [Barcelona]
6 GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC

We investigate extensions of well-known online learning algorithms such as fixed-share of Herbster and Warmuth (1998) or the methods proposed by Bousquet and Warmuth (2002). These algorithms use weight sharing schemes to perform as well as the best sequence of experts with a limited number of changes. Here we show, with a common, general, and simpler analysis, that weight sharing in fact achieves much more than what it was designed for. We use it to simultaneously prove new shifting regret bounds for online convex optimization on the simplex in terms of the total variation distance as well as new bounds for the related setting of adaptive regret. Finally, we exhibit the first logarithmic shifting bounds for exp-concave loss functions on the simplex.

Domaines: Apprentissage [cs.LG]; Machine Learning [stat.ML]

Nicolò Cesa-Bianchi, Pierre Gaillard, Gabor Lugosi, Gilles Stoltz. A new look at shifting regret. 2012. ⟨hal-00670514v1⟩