Uniform regret bounds over $R^d$ for the sequential linear regression problem with the square loss - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2018

Uniform regret bounds over $R^d$ for the sequential linear regression problem with the square loss

Malo Huard
Gilles Stoltz

Résumé

We consider the setting of online linear regression for arbitrary deterministic sequences, with the square loss. We are interested in regret bounds that hold uniformly over all vectors in $u ∈ R^d$. Vovk (2001) showed a d ln T lower bound on this uniform regret. We exhibit forecasters with closed-form regret bounds that match this d ln T quantity. To the best of our knowledge, earlier works only provided closed-form regret bounds of 2d ln T + O(1).
Fichier principal
Vignette du fichier
Gaillard-Gerchinovitz-Huard-Stoltz--Regret-Rd.pdf (284.31 Ko) Télécharger le fichier
Loading...

Dates et versions

hal-01802004 , version 1 (28-05-2018)
hal-01802004 , version 2 (19-02-2019)

Identifiants

Citer

Pierre Gaillard, Sébastien Gerchinovitz, Malo Huard, Gilles Stoltz. Uniform regret bounds over $R^d$ for the sequential linear regression problem with the square loss. 2018. ⟨hal-01802004v1⟩
400 Consultations
327 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More