  We propose a new, simple, and computationally inexpensive termination test
for constant step-size stochastic gradient descent (SGD) applied to binary
classification on the logistic and hinge loss with homogeneous linear
predictors. Our theoretical results support the effectiveness of our stopping
criterion when the data is Gaussian distributed. This presence of noise allows
for the possibility of non-separable data. We show that our test terminates in
a finite number of iterations and when the noise in the data is not too large,
the expected classifier at termination nearly minimizes the probability of
misclassification. Finally, numerical experiments indicate for both real and
synthetic data sets that our termination test exhibits a good degree of
predictability on accuracy and running time.
