# Online Linear Quadratic Control

arXiv: https://arxiv.org/abs/1806.07104 · HTML: https://mlsanity.com/paper/1806.07104/

## Key facts

- Cited by 56 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jun 2018.

## Built on by (most cited first, 30 of 56)

- [Non-stationary Online Learning with Memory and Non-stochastic Control](https://mlsanity.com/paper/2102.03758/) (2021)
- [Meta-Adaptive Nonlinear Control: Theory and Algorithms](https://mlsanity.com/paper/2106.06098/) (2021)
- [Streaming Linear System Identification with Reverse Experience Replay](https://mlsanity.com/paper/2103.05896/) (2021)
- [Learning Mixtures of Linear Dynamical Systems](https://mlsanity.com/paper/2201.11211/) (2022)
- [Adversarial Tracking Control via Strongly Adaptive Online Learning with Memory](https://mlsanity.com/paper/2102.01623/) (2021)
- [Lazy OCO: Online Convex Optimization on a Switching Budget](https://mlsanity.com/paper/2102.03803/) (2021)
- [Identification and Adaptive Control of Markov Jump Systems: Sample Complexity and Regret Bounds](https://mlsanity.com/paper/2111.07018/) (2021)
- [Online Policy Gradient for Model Free Learning of Linear Quadratic Regulators with √T Regret](https://mlsanity.com/paper/2102.12608/) (2021)
- [Sublinear Regret for a Class of Continuous-Time Linear-Quadratic Reinforcement Learning Problems](https://mlsanity.com/paper/2407.17226/) (2024)
- [Learning to Control Linear Systems can be Hard](https://mlsanity.com/paper/2205.14035/) (2022)
- [Provable Sim-to-real Transfer in Continuous Domain with Partial Observations](https://mlsanity.com/paper/2210.15598/) (2022)
- [Smoothed Online Learning for Prediction in Piecewise Affine Systems](https://mlsanity.com/paper/2301.11187/) (2023)
- [A Regret Minimization Approach to Iterative Learning Control](https://mlsanity.com/paper/2102.13478/) (2021)
- [Thompson Sampling Achieves tilde O(√T) Regret in Linear Quadratic Control](https://mlsanity.com/paper/2206.08520/) (2022)
- [Optimal Rates for Bandit Nonstochastic Control](https://mlsanity.com/paper/2305.15352/) (2023)
- [Regret Analysis of Distributed Online LQR Control for Unknown LTI Systems](https://mlsanity.com/paper/2105.07310/) (2021)
- [Optimal Dynamic Regret in LQR Control](https://mlsanity.com/paper/2206.09257/) (2022)
- [Best of Both Worlds in Online Control: Competitive Ratio and Policy Regret](https://mlsanity.com/paper/2211.11219/) (2022)
- [The Sample Complexity of Online Reinforcement Learning: A Multi-model Perspective](https://mlsanity.com/paper/2501.15910/) (2025)
- [Universal Sequence Preconditioning](https://mlsanity.com/paper/2502.06545/) (2025)
- [Rate-Optimal Online Convex Optimization in Adaptive Linear Control](https://mlsanity.com/paper/2206.01426/) (2022)
- [Meta-Learning Online Control for Linear Dynamical Systems](https://mlsanity.com/paper/2208.10259/) (2022)
- [Online Nonstochastic Control with Adversarial and Static Constraints](https://mlsanity.com/paper/2302.02426/) (2023)
- [Oracle-Efficient Smoothed Online Learning for Piecewise Continuous Decision Making](https://mlsanity.com/paper/2302.05430/) (2023)
- [Robust Online Control with Model Misspecification](https://mlsanity.com/paper/2107.07732/) (2021)
- [Finite-time System Identification and Adaptive Control in Autoregressive Exogenous Systems](https://mlsanity.com/paper/2108.11959/) (2021)
- [Dynamic Regret Minimization for Control of Non-stationary Linear Dynamical Systems](https://mlsanity.com/paper/2111.03772/) (2021)
- [Efficient Online Linear Control with Stochastic Convex Costs and Unknown Dynamics](https://mlsanity.com/paper/2203.01170/) (2022)
- [A Nonstochastic Control Approach to Optimization](https://mlsanity.com/paper/2301.07902/) (2023)
- [Stable Online Control of Linear Time-Varying Systems](https://mlsanity.com/paper/2104.14134/) (2021)

## Abstract (arXiv)

We study the problem of controlling linear time-invariant systems with known noisy dynamics and adversarially chosen quadratic losses. We present the first efficient online learning algorithms in this setting that guarantee O(√T) regret under mild assumptions, where T is the time horizon. Our algorithms rely on a novel SDP relaxation for the steady-state distribution of the system. Crucially, and in contrast to previously proposed relaxations, the feasible solutions of our SDP all correspond to "strongly stable" policies that mix exponentially fast to a steady state.