On the Sample Complexity of Noise-Tolerant Learning

In this paper, we further characterize the complexity of noise-tolerant learning in the PAC model. Specifically, we show a general lower bound of Ω ( log(1/δ) ε(1−2η) ) on the number of examples required for PAC learning in the presence of classification noise. Combined with a result of Simon, we effectively show that the sample complexity of PAC learning in the presence of classification noise is Ω ( VC(F) ε(1−2η) + log(1/δ) ε(1−2η) ) . Furthermore, we demonstrate the optimality of the general lower bound by providing a noise-tolerant learning algorithm for the class of symmetric Boolean functions which uses a sample size within a constant factor of this bound. Finally, we note that our general lower bound compares favorably with various general upper bounds for PAC learning in the presence of classification noise.