Second-Order Kernel Online Convex Optimization with Adaptive Sketching

Calandriello, Daniele; Lazaric, Alessandro; Valko, Michal

Type de document :

Communication dans un congrès avec actes

Titre :

Second-Order Kernel Online Convex Optimization with Adaptive Sketching

Auteur(s) :

Calandriello, Daniele [Auteur]
Sequential Learning [SEQUEL]
Lazaric, Alessandro [Auteur]

Sequential Learning [SEQUEL]
Valko, Michal [Auteur]

Sequential Learning [SEQUEL]

Titre de la manifestation scientifique :

International Conference on Machine Learning

Ville :

Sydney

Pays :

Australie

Date de début de la manifestation scientifique :

2017

Discipline(s) HAL :

Statistiques [stat]/Machine Learning [stat.ML]

Résumé en anglais : [en]

Kernel online convex optimization (KOCO) is a framework combining the expressiveness of non-parametric kernel models with the regret guarantees of online learning. First-order KOCO methods such as functional gradient descent ...
Lire la suite >Kernel online convex optimization (KOCO) is a framework combining the expressiveness of non-parametric kernel models with the regret guarantees of online learning. First-order KOCO methods such as functional gradient descent require only $O(t)$ time and space per iteration, and, when the only information on the losses is their convexity, achieve a minimax optimal $O(\sqrt{T})$ regret. Nonetheless, many common losses in kernel problems, such as squared loss, logistic loss, and squared hinge loss posses stronger curvature that can be exploited. In this case, second-order KOCO methods achieve $O(\log(\Det(K)))$ regret, which we show scales as $O(deff \log T)$, where $deff$ is the effective dimension of the problem and is usually much smaller than $O(\sqrt{T})$. The main drawback of second-order methods is their much higher $O(t^2)$ space and time complexity. In this paper, we introduce kernel online Newton step (KONS), a new second-order KOCO method that also achieves $O(deff\log T)$ regret. To address the computational complexity of second-order methods, we introduce a new matrix sketching algorithm for the kernel matrix~$K$, and show that for a chosen parameter $\gamma \leq 1$ our Sketched-KONS reduces the space and time complexity by a factor of $\gamma^2$ to $O(t^2\gamma^2)$ space and time per iteration, while incurring only $1/\gamma$ times more regret.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Projet ANR :

Extraction et transfert de connaissances dans l'apprentissage par renforcement
Inférence bayésienne à ressources limitées - données massives et modèles coûteux

Collections :