Adaptive Methods Are Preferable in High Privacy Settings: An SDE Perspective
Differential Privacy (DP) is becoming central to large-scale training as privacy regulations tighten. We revisit how DP noise interacts with adaptivity in optimization through the lens of stochastic differential equations, providing the first SDE-based analysis of private optimizers. Focusing on DP-SGD and DP-SignSGD under per-example clipping, we show a sharp contrast under fixed hyperparameters: DP-SGD converges at a Privacy-Utility Trade-Off of $\mathcal{O}(1/\varepsilon^2)$ with speed independent of $\varepsilon$, while DP-SignSGD converges at a speed linear in $\varepsilon$ with an $\mathcal{O}(1/\varepsilon)$ trade-off, dominating in high-privacy or large batch noise regimes. By con...
| Authors | Enea Monzio Compagnoni, Alessandro Stanghellini, Rustem Islamov et al. |
|---|---|
| Primary category | cs.LG |
| Published | 3 March 2026 |
| Last updated at source | 3 March 2026 |
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