# Regret Bounds for Robust Adaptive Control of the Linear Quadratic Regulator

arXiv: https://arxiv.org/abs/1805.09388 · HTML: https://mlsanity.com/paper/1805.09388/

## Key facts

- Cited by 86 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2018.

## Built on by (most cited first, 30 of 86)

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- [Thompson Sampling Achieves tilde O(√T) Regret in Linear Quadratic Control](https://mlsanity.com/paper/2206.08520/) (2022)
- [Global Convergence of Two-timescale Actor-Critic for Solving Linear Quadratic Regulator](https://mlsanity.com/paper/2208.08744/) (2022)
- [Learning Dynamical Systems by Leveraging Data from Similar Systems](https://mlsanity.com/paper/2302.04344/) (2023)
- [Sample Complexity of the Linear Quadratic Regulator: A Reinforcement Learning Lens](https://mlsanity.com/paper/2404.10851/) (2024)
- [Adaptive Robust Model Predictive Control with Matched and Unmatched Uncertainty](https://mlsanity.com/paper/2104.08261/) (2021)
- [On the Sample Complexity of Decentralized Linear Quadratic Regulator with Partially Nested Information Structure](https://mlsanity.com/paper/2110.07112/) (2021)
- [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)
- [Provable Regret Bounds for Deep Online Learning and Control](https://mlsanity.com/paper/2110.07807/) (2021)
- [Online Convex Optimization with Unbounded Memory](https://mlsanity.com/paper/2210.09903/) (2022)
- [Best of Both Worlds in Online Control: Competitive Ratio and Policy Regret](https://mlsanity.com/paper/2211.11219/) (2022)

## Abstract (arXiv)

We consider adaptive control of the Linear Quadratic Regulator (LQR), where an unknown linear system is controlled subject to quadratic costs. Leveraging recent developments in the estimation of linear systems and in robust controller synthesis, we present the first provably polynomial time algorithm that provides high probability guarantees of sub-linear regret on this problem. We further study the interplay between regret minimization and parameter estimation by proving a lower bound on the expected regret in terms of the exploration schedule used by any algorithm. Finally, we conduct a numerical study comparing our robust adaptive algorithm to other methods from the adaptive LQR literature, and demonstrate the flexibility of our proposed method by extending it to a demand forecasting problem subject to state constraints.