  Although kernel methods are widely used in many learning problems, they have
poor scalability to large datasets. To address this problem, sketching and
stochastic gradient methods are the most commonly used techniques to derive
efficient large-scale learning algorithms. In this study, we consider solving a
binary classification problem using random features and stochastic gradient
descent. In recent research, an exponential convergence rate of the expected
classification error under the strong low-noise condition has been shown. We
extend these analyses to a random features setting, analyzing the error induced
by the approximation of random features in terms of the distance between the
generated hypothesis including population risk minimizers and empirical risk
minimizers when using general Lipschitz loss functions, to show that an
exponential convergence of the expected classification error is achieved even
if random features approximation is applied. Additionally, we demonstrate that
the convergence rate does not depend on the number of features and there is a
significant computational benefit in using random features in classification
problems because of the strong low-noise condition.
