Precise Convergence Speed of Clipped SGD
We present a tightened convergence analysis of clipped gradient descent on $(L_0, L_1)$-smooth functions, with quantitative constants. Building on the ideas of Koloskova et al (2023), we refactor several case disjunctions to reveal the central role of a control of the bias derived from fundamental properties of $\ell_2$-projection, simplifying proofs. We also extend the domain of validity from $η\leq 1 / (9 β)$ to $η< 1 /β$ where $β= L_0 + c L_1$ for clipping constant $c$, which matches the more traditional analysis of smooth functions. We strengthen the convergence criterion from $\left( \min_{t < T} \mathbb{E}[\lVert \nabla f(x_t) \rVert_2] \right)$ to $\left( \frac{1}{T} \sum_{t < T} \...
| Authors | David A. R. Robin |
|---|---|
| Primary category | cs.LG |
| Published | 24 September 2026 |
| Last updated at source | 24 September 2026 |
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