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We study the problem of boosting the accuracy of a weak learner in the(distribution-independent) PAC model with Massart noise. In the Massart noisemodel, the label of each example $x$ is independently misclassified withprobability $\eta(x) \leq \eta$, where $\eta<1/2$. The Massart model liesbetween the random classification noise model and the agnostic model. Our mainpositive result is the first computationally efficient boosting algorithm inthe presence of Massart noise that achieves misclassification error arbitrarilyclose to $\eta$. Prior to our work, no non-trivial booster was known in thissetting. Moreover, we show that this error upper bound is best possible forpolynomial-time black-box boosters, under standard cryptographic assumptions.Our upper and lower bounds characterize the complexity of boosting in thedistribution-independent PAC model with Massart noise. As a simple applicationof our positive result, we give the first efficient Massart learner for unionsof high-dimensional rectangles.

Boosting in the Presence of Massart Noise