# A Spectral Filtering Approach to Regret Analysis of Distributed Online Control for Linear Dynamical Systems

arXiv: https://arxiv.org/abs/2608.02375 · HTML: https://mlsanity.com/paper/2608.02375/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 40 references that are in the map.
- First posted on arXiv 3 Aug 2026.

## Builds on (most cited first, 24 of 24)

- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [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)
- [Learning Linear Dynamical Systems via Spectral Filtering](https://mlsanity.com/paper/1711.00946/) (2017)
- [Logarithmic Regret for Online Control](https://mlsanity.com/paper/1909.05062/) (2019)
- [Spectral Filtering for General Linear Dynamical Systems](https://mlsanity.com/paper/1802.03981/) (2018)
- [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)
- [On the Regret Analysis of Online LQR Control with Predictions](https://mlsanity.com/paper/2102.01309/) (2021)
- [Spectral State Space Models](https://mlsanity.com/paper/2312.06837/) (2023)
- [Learning the Globally Optimal Distributed LQ Regulator](https://mlsanity.com/paper/1912.08774/) (2019)
- [Optimal Rates for Bandit Nonstochastic Control](https://mlsanity.com/paper/2305.15352/) (2023)
- [Regret Analysis of Distributed Online LQR Control for Unknown LTI Systems](https://mlsanity.com/paper/2105.07310/) (2021)
- [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)
- [Second Order Methods for Bandit Optimization and Control](https://mlsanity.com/paper/2402.08929/) (2024)
- [On the relation between dynamic regret and closed-loop stability](https://mlsanity.com/paper/2209.05964/) (2022)
- [Implications of Regret on Stability of Linear Dynamical Systems](https://mlsanity.com/paper/2211.07411/) (2022)
- [Collaborative Navigation and Manipulation of a Cable-towed Load by Multiple Quadrupedal Robots](https://mlsanity.com/paper/2206.14424/) (2022)
- [A New Approach to Controlling Linear Dynamical Systems](https://mlsanity.com/paper/2504.03952/) (2025)

## Abstract (arXiv)

This paper studies the distributed online control problem over a network of linear time-invariant (LTI) systems in the presence of adversarial disturbances and time-varying convex costs. The network cost is characterized by the summation of local cost functions, where each local function is sequentially revealed only to the corresponding agent. The goal of each agent is to generate a control sequence, using only local observations and neighbor communication, that competes with the best it centralized linear policy in hindsight. We extend the recently proposed Online Spectral Control framework from the centralized setting to the distributed setting. In particular, each agent applies a spectral controller obtained by convolving past disturbances with the leading eigenvectors of a Hankel matrix, while the controller parameters are updated through a distributed online gradient descent step over the local surrogate costs. We formulate this problem this problem as a it regret minimization problem based on the spectral parameterization, and under standard assumptions, we establish a sublinear regret bound of O(frac√Tpoly(log T)γ3), where T is the time horizon and γ denotes the stability margin. The resulting bound also captures the dependence on the network size and connectivity.