# Online Control with Adversarial Disturbances

arXiv: https://arxiv.org/abs/1902.08721 · HTML: https://mlsanity.com/paper/1902.08721/

## Key facts

- Cited by 92 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Feb 2019.

## Built on by (most cited first, 30 of 92)

- [Recurrent Equilibrium Networks: Flexible Dynamic Models with Guaranteed Stability and Robustness](https://mlsanity.com/paper/2104.05942/) (2021)
- [Provable Reinforcement Learning with a Short-Term Memory](https://mlsanity.com/paper/2202.03983/) (2022)
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- [Non-stationary Online Learning with Memory and Non-stochastic Control](https://mlsanity.com/paper/2102.03758/) (2021)
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- [Parameter-free Regret in High Probability with Heavy Tails](https://mlsanity.com/paper/2210.14355/) (2022)
- [Online Learning with Simple Predictors and a Combinatorial Characterization of Minimax in 0/1 Games](https://mlsanity.com/paper/2102.01646/) (2021)
- [Streaming Linear System Identification with Reverse Experience Replay](https://mlsanity.com/paper/2103.05896/) (2021)
- [Online Convex Optimization with Heavy Tails: Old Algorithms, New Regrets, and Applications](https://mlsanity.com/paper/2508.07473/) (2025)
- [Task-Optimal Exploration in Linear Dynamical Systems](https://mlsanity.com/paper/2102.05214/) (2021)
- [Learning-to-learn non-convex piecewise-Lipschitz functions](https://mlsanity.com/paper/2108.08770/) (2021)
- [Efficient Methods for Non-stationary Online Learning](https://mlsanity.com/paper/2309.08911/) (2023)
- [Adversarial Tracking Control via Strongly Adaptive Online Learning with Memory](https://mlsanity.com/paper/2102.01623/) (2021)
- [Lazy OCO: Online Convex Optimization on a Switching Budget](https://mlsanity.com/paper/2102.03803/) (2021)
- [Butterfly Effects of SGD Noise: Error Amplification in Behavior Cloning and Autoregression](https://mlsanity.com/paper/2310.11428/) (2023)
- [Online Control of Unknown Time-Varying Dynamical Systems](https://mlsanity.com/paper/2202.07890/) (2022)
- [Dynamic Regret of Online Markov Decision Processes](https://mlsanity.com/paper/2208.12483/) (2022)
- [Sample-Efficient Linear Representation Learning from Non-IID Non-Isotropic Data](https://mlsanity.com/paper/2308.04428/) (2023)
- [Prospective Artificial Intelligence Approaches for Active Cyber Defence](https://mlsanity.com/paper/2104.09981/) (2021)
- [Safe Adaptive Learning-based Control for Constrained Linear Quadratic Regulators with Regret Guarantees](https://mlsanity.com/paper/2111.00411/) (2021)
- [Deluca -- A Differentiable Control Library: Environments, Methods, and Benchmarking](https://mlsanity.com/paper/2102.09968/) (2021)
- [Regret-optimal Estimation and Control](https://mlsanity.com/paper/2106.12097/) (2021)
- [Non-Linear Reinforcement Learning in Large Action Spaces: Structural Conditions and Sample-efficiency of Posterior Sampling](https://mlsanity.com/paper/2203.08248/) (2022)
- [Learning from Censored and Dependent Data: The case of Linear Dynamics](https://mlsanity.com/paper/2104.05087/) (2021)
- [Optimal Comparator Adaptive Online Learning with Switching Cost](https://mlsanity.com/paper/2205.06846/) (2022)
- [Smoothed Online Learning for Prediction in Piecewise Affine Systems](https://mlsanity.com/paper/2301.11187/) (2023)
- [A Regret Minimization Approach to Iterative Learning Control](https://mlsanity.com/paper/2102.13478/) (2021)
- [Competitive Control](https://mlsanity.com/paper/2107.13657/) (2021)
- [Adversarially Robust PAC Learnability of Real-Valued Functions](https://mlsanity.com/paper/2206.12977/) (2022)
- [Beyond Black-Box Advice: Learning-Augmented Algorithms for MDPs with Q-Value Predictions](https://mlsanity.com/paper/2307.10524/) (2023)

## Abstract (arXiv)

We study the control of a linear dynamical system with adversarial disturbances (as opposed to statistical noise). The objective we consider is one of regret: we desire an online control procedure that can do nearly as well as that of a procedure that has full knowledge of the disturbances in hindsight. Our main result is an efficient algorithm that provides nearly tight regret bounds for this problem. From a technical standpoint, this work generalizes upon previous work in two main aspects: our model allows for adversarial noise in the dynamics, and allows for general convex costs.