In non-smooth stochastic convex optimization, a second epoch of SGD with the standard step size can push the population loss up to a constant, and the paper gives matching rates for any step size and step count.
S tability of S tochastic G radient D escent on N onsmooth C onvex L osses
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Rapid Overfitting of Multi-Pass Stochastic Gradient Descent in Stochastic Convex Optimization
In non-smooth stochastic convex optimization, a second epoch of SGD with the standard step size can push the population loss up to a constant, and the paper gives matching rates for any step size and step count.