A refined primal-dual analysis of the implicit bias
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Recent work shows that gradient descent on linearly separable data is implicitly biased towards the maximum margin solution. However, no convergence rate which is tight in both n (the dataset size) and t (the training time) is given. This work proves that the normalized gradient descent iterates converge to the maximum margin solution at a rate of O(ln(n)/ ln(t)), which is tight in both n and t. The proof is via a dual convergence result: gradient descent induces a multiplicative weights update on the (normalized) SVM dual objective, whose convergence rate leads to the tight implicit bias rate.
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