# Efficient Online Linear Control with Stochastic Convex Costs and Unknown Dynamics

arXiv: https://arxiv.org/abs/2203.01170 · HTML: https://mlsanity.com/paper/2203.01170/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 31 references that are in the map.
- First posted on arXiv 2 Mar 2022.

## Builds on (most cited first, 17 of 17)

- [Naive Exploration is Optimal for Online LQR](https://mlsanity.com/paper/2001.09576/) (2020)
- [Online Control with Adversarial Disturbances](https://mlsanity.com/paper/1902.08721/) (2019)
- [Regret Bounds for Robust Adaptive Control of the Linear Quadratic Regulator](https://mlsanity.com/paper/1805.09388/) (2018)
- [Improper Learning for Non-Stochastic Control](https://mlsanity.com/paper/2001.09254/) (2020)
- [Learning Linear-Quadratic Regulators Efficiently with only √T Regret](https://mlsanity.com/paper/1902.06223/) (2019)
- [Online Linear Quadratic Control](https://mlsanity.com/paper/1806.07104/) (2018)
- [Logarithmic Regret Bound in Partially Observable Linear Dynamical Systems](https://mlsanity.com/paper/2003.11227/) (2020)
- [Black-Box Control for Linear Dynamical Systems](https://mlsanity.com/paper/2007.06650/) (2020)
- [Logarithmic Regret for Adversarial Online Control](https://mlsanity.com/paper/2003.00189/) (2020)
- [Logarithmic Regret for Online Control](https://mlsanity.com/paper/1909.05062/) (2019)
- [Logarithmic Regret for Learning Linear Quadratic Regulators Efficiently](https://mlsanity.com/paper/2002.08095/) (2020)
- [Smoothed Online Optimization for Regression and Control](https://mlsanity.com/paper/1810.10132/) (2018)
- [Making Non-Stochastic Control (Almost) as Easy as Stochastic](https://mlsanity.com/paper/2006.05910/) (2020)
- [Non-Stochastic Control with Bandit Feedback](https://mlsanity.com/paper/2008.05523/) (2020)
- [Efficient Reinforcement Learning for High Dimensional Linear Quadratic Systems](https://mlsanity.com/paper/1303.5984/) (2013)
- [Bandit Linear Control](https://mlsanity.com/paper/2007.00759/) (2020)
- [Geometric Exploration for Online Control](https://mlsanity.com/paper/2010.13178/) (2020)

## Built on by (most cited first, 4 of 4)

- [Rate-Optimal Online Convex Optimization in Adaptive Linear Control](https://mlsanity.com/paper/2206.01426/) (2022)
- [Online Nonstochastic Control with Adversarial and Static Constraints](https://mlsanity.com/paper/2302.02426/) (2023)
- [Scalable LinUCB: Low-Rank Design Matrix Updates for Recommenders with Large Action Spaces](https://mlsanity.com/paper/2510.19349/) (2025)
- [Learning to Control under Time-Varying Environment](https://mlsanity.com/paper/2206.02507/) (2022)

## Abstract (arXiv)

We consider the problem of controlling an unknown linear dynamical system under a stochastic convex cost and full feedback of both the state and cost function. We present a computationally efficient algorithm that attains an optimal √T regret-rate compared to the best stabilizing linear controller in hindsight. In contrast to previous work, our algorithm is based on the Optimism in the Face of Uncertainty paradigm. This results in a substantially improved computational complexity and a simpler analysis.