# Regret Analysis of Distributed Online LQR Control for Unknown LTI Systems arXiv: https://arxiv.org/abs/2105.07310 · HTML: https://mlsanity.com/paper/2105.07310/ ## Key facts - Cited by 6 papers in the map (data through 14 Oct 2026). - Builds on 31 of its 64 references that are in the map. - First posted on arXiv 15 May 2021. ## Builds on (most cited first, 30 of 31) - [Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulator](https://mlsanity.com/paper/1801.05039/) (2018) - [EXTRA: An Exact First-Order Algorithm for Decentralized Consensus Optimization](https://mlsanity.com/paper/1404.6264/) (2014) - [On the Sample Complexity of the Linear Quadratic Regulator](https://mlsanity.com/paper/1710.01688/) (2017) - [Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification](https://mlsanity.com/paper/1802.08334/) (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) - [Near optimal finite time identification of arbitrary linear dynamical systems](https://mlsanity.com/paper/1812.01251/) (2018) - [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) - [Non-asymptotic Identification of LTI Systems from a Single Trajectory](https://mlsanity.com/paper/1806.05722/) (2018) - [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) - [Finite Sample Analysis of Stochastic System Identification](https://mlsanity.com/paper/1903.09122/) (2019) - [Learning Linear Dynamical Systems with Semi-Parametric Least Squares](https://mlsanity.com/paper/1902.00768/) (2019) - [Online Linear Quadratic Control](https://mlsanity.com/paper/1806.07104/) (2018) - [The Nonstochastic Control Problem](https://mlsanity.com/paper/1911.12178/) (2019) - [Learning Linear Dynamical Systems via Spectral Filtering](https://mlsanity.com/paper/1711.00946/) (2017) - [Logarithmic Regret Bound in Partially Observable Linear Dynamical Systems](https://mlsanity.com/paper/2003.11227/) (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) - [Distributed Online Optimization in Dynamic Environments Using Mirror Descent](https://mlsanity.com/paper/1609.02845/) (2016) - [The Power of Predictions in Online Control](https://mlsanity.com/paper/2006.07569/) (2020) - [On the Regret Analysis of Online LQR Control with Predictions](https://mlsanity.com/paper/2102.01309/) (2021) - [Learning the Globally Optimal Distributed LQ Regulator](https://mlsanity.com/paper/1912.08774/) (2019) - [Efficient Reinforcement Learning for High Dimensional Linear Quadratic Systems](https://mlsanity.com/paper/1303.5984/) (2013) - [Learning Partially Observed Linear Dynamical Systems from Logarithmic Number of Samples](https://mlsanity.com/paper/2010.04015/) (2020) - [Distributed Q-Learning for Dynamically Decoupled Systems](https://mlsanity.com/paper/1809.08745/) (2018) - [Distributed Online Linear Quadratic Control for Linear Time-invariant Systems](https://mlsanity.com/paper/2009.13749/) (2020) - [First Order Methods For Globally Optimal Distributed Controllers Beyond Quadratic Invariance](https://mlsanity.com/paper/1909.10999/) (2019) - [A Suboptimality Approach to Distributed Linear Quadratic Optimal Control](https://mlsanity.com/paper/1803.02682/) (2018) ## Built on by (most cited first, 6 of 6) - [Learning the Uncertainty Sets for Control Dynamics via Set Membership: A Non-Asymptotic Analysis](https://mlsanity.com/paper/2309.14648/) (2023) - [Distributed Online System Identification for LTI Systems Using Reverse Experience Replay](https://mlsanity.com/paper/2207.01062/) (2022) - [A Survey on Distributed Online Optimization and Game](https://mlsanity.com/paper/2205.00473/) (2022) - [Regret Analysis of Distributed Online Control for LTI Systems with Adversarial Disturbances](https://mlsanity.com/paper/2310.03206/) (2023) - [Online Multi-Agent Control with Adversarial Disturbances](https://mlsanity.com/paper/2506.18814/) (2025) - [A Spectral Filtering Approach to Regret Analysis of Distributed Online Control for Linear Dynamical Systems](https://mlsanity.com/paper/2608.02375/) (2026) ## Abstract (arXiv) Online optimization has recently opened avenues to study optimal control for time-varying cost functions that are unknown in advance. Inspired by this line of research, we study the distributed online linear quadratic regulator (LQR) problem for linear time-invariant (LTI) systems with unknown dynamics. Consider a multi-agent network where each agent is modeled as a LTI system. The network has a global time-varying quadratic cost, which may evolve adversarially and is only partially observed by each agent sequentially. The goal of the network is to collectively (i) estimate the unknown dynamics and (ii) compute local control sequences competitive to the best centralized policy in hindsight, which minimizes the sum of network costs over time. This problem is formulated as a regret minimization. We propose a distributed variant of the online LQR algorithm, where agents compute their system estimates during an exploration stage. Each agent then applies distributed online gradient descent on a semi-definite programming (SDP) whose feasible set is based on the agent system estimate. We prove that with high probability the regret bound of our proposed algorithm scales as O(T2/3log T), implying the consensus of all agents over time. We also provide simulation results verifying our theoretical guarantee.