Learning Kernel-Based Halfspaces with the Zero-One Loss

Details Learning Kernel-Based Halfspaces with the Zero-One Loss Learning Kernel-Based Halfspaces with the Zero-One Loss

2010-05-20

arxiv.org/abs/1005.3681v2

Computer Science

Learning

This is a full version of the paper appearing in the 23rd International Conference on Learning Theory (COLT 2010). Compared to

Scientific paper

We describe and analyze a new algorithm for agnostically learning kernel-based halfspaces with respect to the \emph{zero-one} loss function. Unlike most previous formulations which rely on surrogate convex loss functions (e.g. hinge-loss in SVM and log-loss in logistic regression), we provide finite time/sample guarantees with respect to the more natural zero-one loss function. The proposed algorithm can learn kernel-based halfspaces in worst-case time $\poly(\exp(L\log(L/\epsilon)))$, for $\emph{any}$ distribution, where $L$ is a Lipschitz constant (which can be thought of as the reciprocal of the margin), and the learned classifier is worse than the optimal halfspace by at most $\epsilon$. We also prove a hardness result, showing that under a certain cryptographic assumption, no algorithm can learn kernel-based halfspaces in time polynomial in $L$.

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