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 in the setup of non-smooth Stochastic Convex Optimization. We show that the generalization error of GD%2C with common choice of hyper-parameters%2C can be %24tilde Theta(d%2Fm %2B 1%2Fsqrt{m})%24%2C where %24d%24 is the dimension and %24m%24 is the sample size. This matches the sample complexity of emph{worst-case} empirical risk minimizers. That means that%2C in contrast with other algorithms%2C GD has no advantage over naive ERMs. Our bound follows from a new generalization bound that depends on both the dimension as well as the learning rate and number of iterations. Our bound also shows that%2C for general hyper-parameters%2C when the dimension is strictly larger than number of samples%2C %24T%3DOmega(1%2Fepsilon^4)%24 iterations are necessary to avoid overfitting. This resolves an open problem by Schlisserman et al.23 and Amir er Al.21%2C and improves over previous lower bounds that demonstrated that the sample size must be at least square root of the dimension.?quality=80&w=800)
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