# Rate-Optimal Online Convex Optimization in Adaptive Linear Control

arXiv: https://arxiv.org/abs/2206.01426 · HTML: https://mlsanity.com/paper/2206.01426/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 45 references that are in the map.
- First posted on arXiv 3 Jun 2022.

## Builds on (most cited first, 22 of 22)

- [Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulator](https://mlsanity.com/paper/1801.05039/) (2018)
- [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)
- [Derivative-Free Methods for Policy Optimization: Guarantees for Linear Quadratic Systems](https://mlsanity.com/paper/1812.08305/) (2018)
- [Online Linear Quadratic Control](https://mlsanity.com/paper/1806.07104/) (2018)
- [Near-optimal Regret Bounds for Stochastic Shortest Path](https://mlsanity.com/paper/2002.09869/) (2020)
- [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)
- [The Gap Between Model-Based and Model-Free Methods on the Linear Quadratic Regulator: An Asymptotic Viewpoint](https://mlsanity.com/paper/1812.03565/) (2018)
- [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)
- [Online learning over a finite action set with limited switching](https://mlsanity.com/paper/1803.01548/) (2018)
- [Non-Stochastic Control with Bandit Feedback](https://mlsanity.com/paper/2008.05523/) (2020)
- [Model-Free Linear Quadratic Control via Reduction to Expert Prediction](https://mlsanity.com/paper/1804.06021/) (2018)
- [Efficient Reinforcement Learning for High Dimensional Linear Quadratic Systems](https://mlsanity.com/paper/1303.5984/) (2013)
- [Online Policy Gradient for Model Free Learning of Linear Quadratic Regulators with √T Regret](https://mlsanity.com/paper/2102.12608/) (2021)
- [Bandit Linear Control](https://mlsanity.com/paper/2007.00759/) (2020)
- [Geometric Exploration for Online Control](https://mlsanity.com/paper/2010.13178/) (2020)
- [Efficient Online Linear Control with Stochastic Convex Costs and Unknown Dynamics](https://mlsanity.com/paper/2203.01170/) (2022)

## Built on by (most cited first, 5 of 5)

- [Online Nonstochastic Model-Free Reinforcement Learning](https://mlsanity.com/paper/2305.17552/) (2023)
- [Regret Analysis of Distributed Online Control for LTI Systems with Adversarial Disturbances](https://mlsanity.com/paper/2310.03206/) (2023)
- [Optimistic Safety for Online Convex Optimization with Unknown Linear Constraints](https://mlsanity.com/paper/2403.05786/) (2024)
- [The Safety-Privacy Tradeoff in Linear Bandits](https://mlsanity.com/paper/2504.16371/) (2025)
- [ASTRA: ADMM-Accelerated Topology Reconfiguration for Dynamic Satellite Constellations](https://mlsanity.com/paper/2609.33993/) (2026)

## Abstract (arXiv)

We consider the problem of controlling an unknown linear dynamical system under adversarially changing convex costs and full feedback of both the state and cost function. We present the first computationally-efficient algorithm that attains an optimal smash√T-regret rate compared to the best stabilizing linear controller in hindsight, while avoiding stringent assumptions on the costs such as strong convexity. Our approach is based on a careful design of non-convex lower confidence bounds for the online costs, and uses a novel technique for computationally-efficient regret minimization of these bounds that leverages their particular non-convex structure.