# Adaptive Control of Differentially Private Linear Quadratic Systems

arXiv: https://arxiv.org/abs/2108.11563 · HTML: https://mlsanity.com/paper/2108.11563/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 29 references that are in the map.
- First posted on arXiv 26 Aug 2021.

## Builds on (most cited first, 12 of 12)

- [Provably Efficient Reinforcement Learning with Linear Function Approximation](https://mlsanity.com/paper/1907.05388/) (2019)
- [Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds](https://mlsanity.com/paper/1605.02065/) (2016)
- [Model-based Reinforcement Learning and the Eluder Dimension](https://mlsanity.com/paper/1406.1853/) (2014)
- [Private Reinforcement Learning with PAC and Regret Guarantees](https://mlsanity.com/paper/2009.09052/) (2020)
- [Algorithms for Differentially Private Multi-Armed Bandits](https://mlsanity.com/paper/1511.08681/) (2015)
- [On Online Learning in Kernelized Markov Decision Processes](https://mlsanity.com/paper/1911.01871/) (2019)
- [Differential Privacy for Multi-armed Bandits: What Is It and What Is Its Cost?](https://mlsanity.com/paper/1905.12298/) (2019)
- [Achieving Privacy in the Adversarial Multi-Armed Bandit](https://mlsanity.com/paper/1701.04222/) (2017)
- [Private Matchings and Allocations](https://mlsanity.com/paper/1311.2828/) (2013)
- [Differentially Private Policy Evaluation](https://mlsanity.com/paper/1603.02010/) (2016)
- [Local Differential Privacy for Bayesian Optimization](https://mlsanity.com/paper/2010.06709/) (2020)
- [Episodic Linear Quadratic Regulators with Low-rank Transitions](https://mlsanity.com/paper/2011.01568/) (2020)

## Built on by (most cited first, 7 of 7)

- [Shuffle Private Linear Contextual Bandits](https://mlsanity.com/paper/2202.05567/) (2022)
- [Differentially Private Regret Minimization in Episodic Markov Decision Processes](https://mlsanity.com/paper/2112.10599/) (2021)
- [Differentially Private Reinforcement Learning with Linear Function Approximation](https://mlsanity.com/paper/2201.07052/) (2022)
- [Offline Reinforcement Learning with Differential Privacy](https://mlsanity.com/paper/2206.00810/) (2022)
- [Distributed Differential Privacy in Multi-Armed Bandits](https://mlsanity.com/paper/2206.05772/) (2022)
- [Differentially Private Reinforcement Learning with Self-Play](https://mlsanity.com/paper/2404.07559/) (2024)
- [Learning to Control under Time-Varying Environment](https://mlsanity.com/paper/2206.02507/) (2022)

## Abstract (arXiv)

In this paper, we study the problem of regret minimization in reinforcement learning (RL) under differential privacy constraints. This work is motivated by the wide range of RL applications for providing personalized service, where privacy concerns are becoming paramount. In contrast to previous works, we take the first step towards non-tabular RL settings, while providing a rigorous privacy guarantee. In particular, we consider the adaptive control of differentially private linear quadratic (LQ) systems. We develop the first private RL algorithm, PRL, which is able to attain a sub-linear regret while guaranteeing privacy protection. More importantly, the additional cost due to privacy is only on the order of fracln(1/δ)1/4ε1/2 given privacy parameters ε, δ > 0. Through this process, we also provide a general procedure for adaptive control of LQ systems under changing regularizers, which not only generalizes previous non-private controls, but also serves as the basis for general private controls.