A termination criterion for stochastic gradient descent for binary classification

• URL: http://arxiv.org/abs/2003.10312v1
• Date: Mon, 23 Mar 2020 15:00:21 GMT
• Title: A termination criterion for stochastic gradient descent for binary classification
• Authors: Sina Baghal, Courtney Paquette, Stephen A. Vavasis
• Abstract summary: We propose a new, simple, and inexpensive termination test for constant step-size gradient descent. 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.
• Score: 3.216356957608319
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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