# Privacy-Preserving Distributed Online Mirror Descent for Nonconvex Optimization

arXiv: https://arxiv.org/abs/2501.04222 · HTML: https://mlsanity.com/paper/2501.04222/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jan 2025.

## Built on by (most cited first, 1 of 1)

- [A New Kernel Regularity Condition for Distributed Mirror Descent: Broader Coverage and Simpler Analysis](https://mlsanity.com/paper/2603.12838/) (2026)

## Abstract (arXiv)

We investigate the distributed online nonconvex optimization problem with differential privacy over time-varying networks. Each node minimizes the sum of several nonconvex functions while preserving the node's differential privacy. We propose a privacy-preserving distributed online mirror descent algorithm for nonconvex optimization, which uses the mirror descent to update decision variables and the Laplace differential privacy mechanism to protect privacy. Unlike the existing works, the proposed algorithm allows the cost functions to be nonconvex, which is more applicable. Based upon these, we prove that if the communication network is B-strongly connected and the constraint set is compact, then by choosing the step size properly, the algorithm guarantees ε-differential privacy at each time. Furthermore, we prove that if the local cost functions are β-smooth, then the regret over time horizon T grows sublinearly while preserving differential privacy, with an upper bound O(√T). Finally, the effectiveness of the algorithm is demonstrated through numerical simulations.