Second-Order Kernel Online Convex Optimization with Adaptive Sketching

Calandriello, Daniele; Lazaric, Alessandro; Valko, Michal

Document type :

Communication dans un congrès avec actes

Title :

Second-Order Kernel Online Convex Optimization with Adaptive Sketching

Author(s) :

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

Sequential Learning [SEQUEL]

Conference title :

International Conference on Machine Learning

City :

Sydney

Country :

Australie

Start date of the conference :

2017

HAL domain(s) :

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

English abstract : [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 ...
Show more >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.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

ANR Project :

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

Collections :