We study a private variant of ADMM with (strongly) convex objective functions. We consider a privacy model in which each iteration corresponds to a user whose private function is accessed only to update the primal variable, which is masked with Gaussian noise to achieve local privacy, while no noise is directly added to the dual variable. 

Privacy amplification by iteration can be interpreted from the perspective of the user from the first iteration. A recent work by Cyffers et al. [ICML 2023] has investigated privacy amplification by iteration for the proximal variant of ADMM, in which the entire private function of a user is accessed. In contrast, we consider a private variant of ADMM that needs only one gradient access to a user's private function. However, in this variant, both the primal and the dual variables need to be passed between successive iterations.

In order to apply the coupling framework in Balle et al. [NeurIPS 2019] to this gradient variant of ADMM, we need some novel ideas to resolve the following technical hurdles. First, we need that each ADMM iteration corresponds to a non-expansive mapping that unfortunately does not hold under the usual norm on the joint space of the primal and the dual variables, which we resolve by considering a customized norm.  Second, since the dual variable is not masked with any noise in each iteration, one iteration of noisy ADMM does not have a strong enough privacy guarantee, which we resolve by considering two consecutive noisy ADMM iterations together as a Markov operator.  

Our main result is that the privacy guarantee for the gradient variant of ADMM can be amplified by a factor proportional to the number of iterations; for strongly convex objective functions, the amplification is exponential in the number of iterations. These amplification results are consistent with the previous special case of stochastic gradient descent.

Privacy Amplification by Iteration for ADMM with (Strongly) Convex Objective Functions

Main Track - Machine Learning

technical paper

We are pleased to announce the Thirty-Eighth AAAI Conference on Artificial Intelligence (AAAI-24), which will be held in Vancouver, British Columbia at the Vancouver Convention Centre – West Building from 20-27 February, 2024.

The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines. AAAI-24 will feature technical paper presentations, special tracks, invited speakers, workshops, tutorials, poster sessions, senior member presentations, competitions, and exhibit programs, and a range of other activities to be announced.

We expect for AAAI-24 to be an in-person conference – one author of all accepted papers will be expected to present work in person unless there are exceptional circumstances that prevent this.<br><br><br><br>

In order to access the AAAI-24 event page you need to register [here](https://aaai.org/aaai-conference/registration/)

AAAI 2024

The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines. 

T-H. Hubert Chan

1

12

SHORT BIO

Presentations

Privacy Amplification by Iteration for ADMM with (Strongly) Convex Objective Functions

Stay up to date with the latest Underline news!

PRESENTATIONS

CONFERENCES

COMPANY

RESOURCES