Online learning of noisy data with kernels

Nicolò Cesa-Bianchi, Shai Shalev Shwartz, Ohad Shamir

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

11 Scopus citations


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 dotproduct (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.

Original languageAmerican English
Title of host publicationCOLT 2010 - The 23rd Conference on Learning Theory
Number of pages13
StatePublished - 2010
Event23rd Conference on Learning Theory, COLT 2010 - Haifa, Israel
Duration: 27 Jun 201029 Jun 2010

Publication series

NameCOLT 2010 - The 23rd Conference on Learning Theory


Conference23rd Conference on Learning Theory, COLT 2010


Dive into the research topics of 'Online learning of noisy data with kernels'. Together they form a unique fingerprint.

Cite this