For smooth convex functions, relatively inexact gradient descent has a three-regime worst-case one-step rate, and the largest provably safe stepsize is 2/(1+delta).
d’Aspremont, Smooth optimization with approximate gradient
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Worst-case convergence analysis of relatively inexact gradient descent on smooth convex functions
For smooth convex functions, relatively inexact gradient descent has a three-regime worst-case one-step rate, and the largest provably safe stepsize is 2/(1+delta).