Near-Optimal Last-Iterate Convergence of SGD in the Smooth Interpolation Regime
We study the last iterate of stochastic gradient descent (SGD) with a constant stepsize on smooth convex objectives in the low-noise and interpolation regimes, where the variance $σ_\star^2$ of the stochastic gradients at the optimum is small or zero. We establish that after $T$ steps of SGD on $β$-smooth convex losses with any constant stepsize $0<η<2/β$, the last iterate attains expected excess risk $\widetilde O\bigl(\tfrac{1}{η(2-βη)^3T}+\tfracη{(2-βη)^4}σ_\star^2\bigr)$, which gives the rate $\smash{\widetilde O(1/T)}$ for every constant stepsize in the interpolation regime ($σ_\star=0$), matching the $Ω(1/T)$ lower bound up to logarithmic factors and improving upon the $O(1/\sqrt T)...
| Authors | Matan Schliserman, Tomer Koren |
|---|---|
| Primary category | cs.LG |
| Published | 18 October 2026 |
| Last updated at source | 18 October 2026 |
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