# The Nonstochastic Control Problem

arXiv: https://arxiv.org/abs/1911.12178 · HTML: https://mlsanity.com/paper/1911.12178/

## Key facts

- Cited by 52 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Nov 2019.

## Built on by (most cited first, 30 of 52)

- [Online DPO: Online Direct Preference Optimization with Fast-Slow Chasing](https://mlsanity.com/paper/2406.05534/) (2024)
- [Non-stationary Online Learning with Memory and Non-stochastic Control](https://mlsanity.com/paper/2102.03758/) (2021)
- [Stabilizing Dynamical Systems via Policy Gradient Methods](https://mlsanity.com/paper/2110.06418/) (2021)
- [Streaming Linear System Identification with Reverse Experience Replay](https://mlsanity.com/paper/2103.05896/) (2021)
- [Efficient Methods for Non-stationary Online Learning](https://mlsanity.com/paper/2309.08911/) (2023)
- [Generative Models in Decision Making: A Survey](https://mlsanity.com/paper/2502.17100/) (2025)
- [Learning over All Stabilizing Nonlinear Controllers for a Partially-Observed Linear System](https://mlsanity.com/paper/2112.04219/) (2021)
- [Online Control of Unknown Time-Varying Dynamical Systems](https://mlsanity.com/paper/2202.07890/) (2022)
- [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)
- [Learning from Censored and Dependent Data: The case of Linear Dynamics](https://mlsanity.com/paper/2104.05087/) (2021)
- [A Regret Minimization Approach to Iterative Learning Control](https://mlsanity.com/paper/2102.13478/) (2021)
- [Competitive Control](https://mlsanity.com/paper/2107.13657/) (2021)
- [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)
- [Adaptive Composite Online Optimization: Predictions in Static and Dynamic Environments](https://mlsanity.com/paper/2205.00446/) (2022)
- [Optimal Dynamic Regret in LQR Control](https://mlsanity.com/paper/2206.09257/) (2022)
- [Online Convex Optimization with Unbounded Memory](https://mlsanity.com/paper/2210.09903/) (2022)
- [Best of Both Worlds in Online Control: Competitive Ratio and Policy Regret](https://mlsanity.com/paper/2211.11219/) (2022)
- [Nonasymptotic Regret Analysis of Adaptive Linear Quadratic Control with Model Misspecification](https://mlsanity.com/paper/2401.00073/) (2023)
- [The Sample Complexity of Online Reinforcement Learning: A Multi-model Perspective](https://mlsanity.com/paper/2501.15910/) (2025)
- [DiffLoop: Tuning PID controllers by differentiating through the feedback loop](https://mlsanity.com/paper/2106.10516/) (2021)
- [Meta-Learning Online Control for Linear Dynamical Systems](https://mlsanity.com/paper/2208.10259/) (2022)
- [Efficient Online Learning with Memory via Frank-Wolfe Optimization: Algorithms with Bounded Dynamic Regret and Applications to Control](https://mlsanity.com/paper/2301.00497/) (2023)
- [Universal Learning of Nonlinear Dynamics](https://mlsanity.com/paper/2508.11990/) (2025)
- [Robust Online Control with Model Misspecification](https://mlsanity.com/paper/2107.07732/) (2021)
- [Dynamic Regret Minimization for Control of Non-stationary Linear Dynamical Systems](https://mlsanity.com/paper/2111.03772/) (2021)
- [Regret Analysis of Multi-task Representation Learning for Linear-Quadratic Adaptive Control](https://mlsanity.com/paper/2407.05781/) (2024)
- [Online Learning for Predictive Control with Provable Regret Guarantees](https://mlsanity.com/paper/2111.15041/) (2021)
- [Adaptive Online Non-stochastic Control](https://mlsanity.com/paper/2310.02261/) (2023)

## Abstract (arXiv)

We consider the problem of controlling an unknown linear dynamical system in the presence of (nonstochastic) adversarial perturbations and adversarial convex loss functions. In contrast to classical control, the a priori determination of an optimal controller here is hindered by the latter's dependence on the yet unknown perturbations and costs. Instead, we measure regret against an optimal linear policy in hindsight, and give the first efficient algorithm that guarantees a sublinear regret bound, scaling as T^{2/3}, in this setting.