# Regret Analysis of Distributed Online Control for LTI Systems with Adversarial Disturbances

arXiv: https://arxiv.org/abs/2310.03206 · HTML: https://mlsanity.com/paper/2310.03206/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 53 references that are in the map.
- First posted on arXiv 4 Oct 2023.

## Builds on (most cited first, 30 of 35)

- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [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)
- [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)
- [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 Online Control](https://mlsanity.com/paper/1909.05062/) (2019)
- [Adaptive Regret for Control of Time-Varying Dynamics](https://mlsanity.com/paper/2007.04393/) (2020)
- [Logarithmic Regret for Learning Linear Quadratic Regulators Efficiently](https://mlsanity.com/paper/2002.08095/) (2020)
- [The Power of Predictions in Online Control](https://mlsanity.com/paper/2006.07569/) (2020)
- [An Online Learning Approach to Model Predictive Control](https://mlsanity.com/paper/1902.08967/) (2019)
- [On the Regret Analysis of Online LQR Control with Predictions](https://mlsanity.com/paper/2102.01309/) (2021)
- [Reinforcement Learning with Fast Stabilization in Linear Dynamical Systems](https://mlsanity.com/paper/2007.12291/) (2020)
- [Streaming Linear System Identification with Reverse Experience Replay](https://mlsanity.com/paper/2103.05896/) (2021)
- [Near-optimal Offline and Streaming Algorithms for Learning Non-Linear Dynamical Systems](https://mlsanity.com/paper/2105.11558/) (2021)
- [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)
- [Regret Analysis of Distributed Online LQR Control for Unknown LTI Systems](https://mlsanity.com/paper/2105.07310/) (2021)
- [Distributed Online Linear Quadratic Control for Linear Time-invariant Systems](https://mlsanity.com/paper/2009.13749/) (2020)
- [Rate-Optimal Online Convex Optimization in Adaptive Linear Control](https://mlsanity.com/paper/2206.01426/) (2022)

## Built on by (most cited first, 1 of 1)

- [Online Multi-Agent Control with Adversarial Disturbances](https://mlsanity.com/paper/2506.18814/) (2025)

## Abstract (arXiv)

This paper addresses the distributed online control problem over a network of linear time-invariant (LTI) systems (with possibly unknown dynamics) in the presence of adversarial perturbations. There exists a global network cost that is characterized by a time-varying convex function, which evolves in an adversarial manner and is sequentially and partially observed by local agents. The goal of each agent is to generate a control sequence that can compete with the best centralized control policy in hindsight, which has access to the global cost. This problem is formulated as a regret minimization. For the case of known dynamics, we propose a fully distributed disturbance feedback controller that guarantees a regret bound of O(√Tlog T), where T is the time horizon. For the unknown dynamics case, we design a distributed explore-then-commit approach, where in the exploration phase all agents jointly learn the system dynamics, and in the learning phase our proposed control algorithm is applied using each agent system estimate. We establish a regret bound of O(T2/3 poly(log T)) for this setting.