## Learning large-margin halfspaces with more malicious noise

Citations: | 1 - 0 self |

### BibTeX

@MISC{Long_learninglarge-margin,

author = {Philip M. Long and Rocco A. Servedio},

title = {Learning large-margin halfspaces with more malicious noise},

year = {}

}

### OpenURL

### Abstract

We describe a simple algorithm that runs in time poly(n, 1/γ, 1/ε) and learns an unknown n-dimensional γ-margin halfspace to accuracy 1 − ε in the presence of malicious noise, when the noise rate is allowed to be as high as Θ(εγ √ log(1/γ)). Previous efficient algorithms could only learn to accuracy ε in the presence of malicious noise of rate at most Θ(εγ). Our algorithm does not work by optimizing a convex loss function. We show that no algorithm for learning γ-margin halfspaces that minimizes a convex proxy for misclassification error can tolerate malicious noise at a rate greater than Θ(εγ); this may partially explain why previous algorithms could not achieve the higher noise tolerance of our new algorithm. 1