Differentially private accelerated optimization algorithms

SIAM Journal on Optimization, 32(2), pp. 795–821, 2022.

Publisher (DOI)arXiv:2008.01989

Differentially private versions of the accelerated first-order methods. A smoothing approach keeps the privacy noise injected into heavy-ball iterations from accumulating, and a noise-dividing mechanism does the same for Nesterov’s method and its multistage variant; dynamical-systems analysis gives convergence rates for both, showing that acceleration survives the privacy constraint and improves the utility achievable at a given privacy budget.

Differential privacyMomentum & acceleration

• Rényi differential privacy for heavy-tailed SDEs via fractional Poincaré inequalities (arXiv, 2025)
• Differential privacy of noisy (S)GD under heavy-tailed perturbations (arXiv, 2024)
• Accelerated gradient methods for nonconvex optimization: escape trajectories from strict saddle points and convergence to local minima (Found. Comput. Math., 2026)
• Accelerated gradient methods with biased gradient estimates: risk sensitivity, high-probability guarantees, and large deviation bounds (J. Nonlinear Var. Anal., 2026)
• Algorithmic stability of stochastic gradient descent with momentum under heavy-tailed noise (arXiv, 2025)