Mirror Descent Algorithms with Nearly Dimension-Independent Rates for Differentially-Private Stochastic Saddle-Point Problems

no code implementations • 5 Mar 2024 • Tomás González, Cristóbal Guzmán, Courtney Paquette

For convex-concave and first-order-smooth stochastic objectives, our algorithms attain a rate of $\sqrt{\log(d)/n} + (\log(d)^{3/2}/[n\varepsilon])^{1/3}$, where $d$ is the dimension of the problem and $n$ the dataset size.

LEMMA

Faster Rates of Convergence to Stationary Points in Differentially Private Optimization

no code implementations • 2 Jun 2022 • Raman Arora, Raef Bassily, Tomás González, Cristóbal Guzmán, Michael Menart, Enayat Ullah

We provide a new efficient algorithm that finds an $\tilde{O}\big(\big[\frac{\sqrt{d}}{n\varepsilon}\big]^{2/3}\big)$-stationary point in the finite-sum setting, where $n$ is the number of samples.

Stochastic Optimization