# Differentially Private LQ Control

arXiv: https://arxiv.org/abs/1807.05082 · HTML: https://mlsanity.com/paper/1807.05082/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jul 2018.

## Built on by (most cited first, 3 of 3)

- [Striking a Balance: An Optimal Mechanism Design for Heterogenous Differentially Private Data Acquisition for Logistic Regression](https://mlsanity.com/paper/2309.10340/) (2023)
- [Privacy-Preserving Reinforcement Learning Beyond Expectation](https://mlsanity.com/paper/2203.10165/) (2022)
- [Deceptive Sequential Decision-Making via Regularized Policy Optimization](https://mlsanity.com/paper/2501.18803/) (2025)

## Abstract (arXiv)

As multi-agent systems proliferate and share more user data, new approaches are needed to protect sensitive data while still enabling system operation. To address this need, this paper presents a private multi-agent LQ control framework. Agents' state trajectories can be sensitive and we therefore protect them using differential privacy. We quantify the impact of privacy along three dimensions: the amount of information shared under privacy, the control-theoretic cost of privacy, and the tradeoffs between privacy and performance. These analyses are done in conventional control-theoretic terms, which we use to develop guidelines for calibrating privacy as a function of system parameters. Numerical results indicate that system performance remains within desirable ranges, even under strict privacy requirements.