Learning large-margin halfspaces with more malicious noise

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.