Gradient Descent's Last Iterate is Often (slightly) Suboptimal
We consider the well-studied setting of minimizing a convex Lipschitz function using either gradient descent (GD) or its stochastic variant (SGD), and examine the last iterate convergence. By now, it is known that standard stepsize choices lead to a last iterate convergence rate of $\log T/\sqrt{T}$ after $T$ steps. A breakthrough result of Jain et al. [2019] recovered the optimal $1/\sqrt{T}$ rate by constructing a non-standard stepsize sequence. However, this sequence requires choosing $T$ in advance, as opposed to common stepsize schedules which apply for any time horizon. Moreover, Jain et al. conjectured that without prior knowledge of $T$, no stepsize sequence can ensure the optimal...
| Authors | Guy Kornowski, Ohad Shamir |
|---|---|
| Primary category | math.OC |
| Published | 15 April 2026 |
| Last updated at source | 2 October 2026 |
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