# Certainty Equivalence is Efficient for Linear Quadratic Control

arXiv: https://arxiv.org/abs/1902.07826 · HTML: https://mlsanity.com/paper/1902.07826/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Feb 2019.

## Built on by (most cited first, 13 of 13)

- [Provably Efficient Reinforcement Learning in Partially Observable Dynamical Systems](https://mlsanity.com/paper/2206.12020/) (2022)
- [Exploration-exploitation trade-off for continuous-time episodic reinforcement learning with linear-convex models](https://mlsanity.com/paper/2112.10264/) (2021)
- [Task-Optimal Exploration in Linear Dynamical Systems](https://mlsanity.com/paper/2102.05214/) (2021)
- [PC-MLP: Model-based Reinforcement Learning with Policy Cover Guided Exploration](https://mlsanity.com/paper/2107.07410/) (2021)
- [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)
- [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 scheduling of entropy regulariser for continuous-time linear-quadratic reinforcement learning](https://mlsanity.com/paper/2208.04466/) (2022)
- [Finite-time System Identification and Adaptive Control in Autoregressive Exogenous Systems](https://mlsanity.com/paper/2108.11959/) (2021)
- [Scalable regret for learning to control network-coupled subsystems with unknown dynamics](https://mlsanity.com/paper/2108.07970/) (2021)
- [A relaxed technical assumption for posterior sampling-based reinforcement learning for control of unknown linear systems](https://mlsanity.com/paper/2108.08502/) (2021)
- [On the Effectiveness of Iterative Learning Control](https://mlsanity.com/paper/2111.09434/) (2021)

## Abstract (arXiv)

We study the performance of the certainty equivalent controller on Linear Quadratic (LQ) control problems with unknown transition dynamics. We show that for both the fully and partially observed settings, the sub-optimality gap between the cost incurred by playing the certainty equivalent controller on the true system and the cost incurred by using the optimal LQ controller enjoys a fast statistical rate, scaling as the square of the parameter error. To the best of our knowledge, our result is the first sub-optimality guarantee in the partially observed Linear Quadratic Gaussian (LQG) setting. Furthermore, in the fully observed Linear Quadratic Regulator (LQR), our result improves upon recent work by Dean et al. (2017), who present an algorithm achieving a sub-optimality gap linear in the parameter error. A key part of our analysis relies on perturbation bounds for discrete Riccati equations. We provide two new perturbation bounds, one that expands on an existing result from Konstantinov et al. (1993), and another based on a new elementary proof strategy.