TY - GEN

T1 - Online learning of noisy data with kernels

AU - Cesa-Bianchi, Nicolò

AU - Shwartz, Shai Shalev

AU - Shamir, Ohad

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84870176618&partnerID=8YFLogxK

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AN - SCOPUS:84870176618

SN - 9780982252925

T3 - COLT 2010 - The 23rd Conference on Learning Theory

SP - 218

EP - 230

BT - COLT 2010 - The 23rd Conference on Learning Theory

T2 - 23rd Conference on Learning Theory, COLT 2010

Y2 - 27 June 2010 through 29 June 2010

ER -