mlsanityData to 7 Oct 2026

Adaptive Control of Differentially Private Linear Quadratic Systems

arXiv 2108.11563 ↗First posted 26 Aug 2021cs.LGcited by 7

Not on the map. Why?

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.

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

Builds on

12 of 29 references.

References · 12

  1. 2019Provably Efficient Reinforcement Learning with Linear Function Approximationcited by 514
  2. 2016Concentrated Differential Privacy: Simplifications, Extensions, and Lower Boundscited by 339
  3. 2014Model-based Reinforcement Learning and the Eluder Dimensioncited by 116
  4. 2020Private Reinforcement Learning with PAC and Regret Guaranteescited by 51
  5. 2015Algorithms for Differentially Private Multi-Armed Banditscited by 44
  6. 2019On Online Learning in Kernelized Markov Decision Processescited by 32
  7. 2019Differential Privacy for Multi-armed Bandits: What Is It and What Is Its Cost?cited by 27
  8. 2017Achieving Privacy in the Adversarial Multi-Armed Banditcited by 24
  9. 2013Private Matchings and Allocationscited by 23
  10. 2016Differentially Private Policy Evaluationcited by 19
  11. 2020Local Differential Privacy for Bayesian Optimizationcited by 19
  12. 2020Episodic Linear Quadratic Regulators with Low-rank Transitionscited by 3

Built on by

Cited by year

Citing papers per year: 2021: 1; 2022: 5; 2023: 0; 2024: 1.

7 papers.

  1. 2022Shuffle Private Linear Contextual Banditscited by 27
  2. 2021Differentially Private Regret Minimization in Episodic Markov Decision Processescited by 23
  3. 2022Differentially Private Reinforcement Learning with Linear Function Approximationcited by 22
  4. 2022Offline Reinforcement Learning with Differential Privacycited by 19
  5. 2022Distributed Differential Privacy in Multi-Armed Banditscited by 14
  6. 2024Differentially Private Reinforcement Learning with Self-Playcited by 1
  7. 2022Learning to Control under Time-Varying Environmentcited by 0