Online Learning of Noisy Data with Kernels

Details Online Learning of Noisy Data with Kernels Online Learning of Noisy Data with Kernels

2010-05-13

arxiv.org/abs/1005.2296v2

Computer Science

Learning

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

Scientific paper

We study online learning when individual instances are corrupted by adversarially chosen random noise. We assume the noise distribution is unknown, and may change over time with no restriction other than having zero mean and bounded variance. Our technique relies on a family of unbiased estimators for non-linear functions, which may be of independent interest. We show that a variant of online gradient descent can learn functions in any dot-product (e.g., polynomial) or Gaussian kernel space with any analytic convex loss function. Our variant uses randomized estimates that need to query a random number of noisy copies of each instance, where with high probability this number is upper bounded by a constant. Allowing such multiple queries cannot be avoided: Indeed, we show that online learning is in general impossible when only one noisy copy of each instance can be accessed.

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