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We prove bounds on the population risk of the maximum margin algorithm fortwo-class linear classification. For linearly separable training data, themaximum margin algorithm has been shown in previous work to be equivalent to alimit of training with logistic loss using gradient descent, as the trainingerror is driven to zero. We analyze this algorithm applied to random dataincluding misclassification noise. Our assumptions on the clean data includethe case in which the class-conditional distributions are standard normaldistributions. The misclassification noise may be chosen by an adversary,subject to a limit on the fraction of corrupted labels. Our bounds show that,with sufficient over-parameterization, the maximum margin algorithm trained onnoisy data can achieve nearly optimal population risk.

Finite-sample Analysis of Interpolating Linear Classifiers in the Overparameterized Regime