# Online Nonstochastic Control with Adversarial and Static Constraints

arXiv: https://arxiv.org/abs/2302.02426 · HTML: https://mlsanity.com/paper/2302.02426/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 56 references that are in the map.
- First posted on arXiv 5 Feb 2023.

## Builds on (most cited first, 30 of 39)

- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [End-to-End Safe Reinforcement Learning through Barrier Functions for Safety-Critical Continuous Control Tasks](https://mlsanity.com/paper/1903.08792/) (2019)
- [A General Safety Framework for Learning-Based Control in Uncertain Robotic Systems](https://mlsanity.com/paper/1705.01292/) (2017)
- [Exploration-Exploitation in Constrained MDPs](https://mlsanity.com/paper/2003.02189/) (2020)
- [Provably Efficient Safe Exploration via Primal-Dual Policy Optimization](https://mlsanity.com/paper/2003.00534/) (2020)
- [Learning-based Model Predictive Control for Safe Exploration](https://mlsanity.com/paper/1803.08287/) (2018)
- [Online Convex Optimization with Stochastic Constraints](https://mlsanity.com/paper/1708.03741/) (2017)
- [Online Control with Adversarial Disturbances](https://mlsanity.com/paper/1902.08721/) (2019)
- [Neural-Fly Enables Rapid Learning for Agile Flight in Strong Winds](https://mlsanity.com/paper/2205.06908/) (2022)
- [Improper Learning for Non-Stochastic Control](https://mlsanity.com/paper/2001.09254/) (2020)
- [Learning Policies with Zero or Bounded Constraint Violation for Constrained MDPs](https://mlsanity.com/paper/2106.02684/) (2021)
- [Online Convex Optimization with Time-Varying Constraints](https://mlsanity.com/paper/1702.04783/) (2017)
- [Online Linear Quadratic Control](https://mlsanity.com/paper/1806.07104/) (2018)
- [Learning nonlinear dynamical systems from a single trajectory](https://mlsanity.com/paper/2004.14681/) (2020)
- [Logarithmic Regret for Adversarial Online Control](https://mlsanity.com/paper/2003.00189/) (2020)
- [Regret and Cumulative Constraint Violation Analysis for Online Convex Optimization with Long Term Constraints](https://mlsanity.com/paper/2106.05135/) (2021)
- [Logarithmic Regret for Online Control](https://mlsanity.com/paper/1909.05062/) (2019)
- [Linear model predictive safety certification for learning-based control](https://mlsanity.com/paper/1803.08552/) (2018)
- [Near-Optimal Sample Complexity Bounds for Constrained MDPs](https://mlsanity.com/paper/2206.06270/) (2022)
- [Safe Reinforcement Learning with Linear Function Approximation](https://mlsanity.com/paper/2106.06239/) (2021)
- [Safely Learning to Control the Constrained Linear Quadratic Regulator](https://mlsanity.com/paper/1809.10121/) (2018)
- [Provably Efficient Model-Free Constrained RL with Linear Function Approximation](https://mlsanity.com/paper/2206.11889/) (2022)
- [An Efficient Pessimistic-Optimistic Algorithm for Stochastic Linear Bandits with General Constraints](https://mlsanity.com/paper/2102.05295/) (2021)
- [Learning Infinite-Horizon Average-Reward Markov Decision Processes with Constraints](https://mlsanity.com/paper/2202.00150/) (2022)
- [Regret and Cumulative Constraint Violation Analysis for Distributed Online Constrained Convex Optimization](https://mlsanity.com/paper/2105.00321/) (2021)
- [Online Optimal Control with Affine Constraints](https://mlsanity.com/paper/2010.04891/) (2020)
- [Introduction to Online Control](https://mlsanity.com/paper/2211.09619/) (2022)
- [Non-Stochastic Control with Bandit Feedback](https://mlsanity.com/paper/2008.05523/) (2020)

## Built on by (most cited first, 5 of 5)

- [Learning the Uncertainty Sets for Control Dynamics via Set Membership: A Non-Asymptotic Analysis](https://mlsanity.com/paper/2309.14648/) (2023)
- [Adaptive Online Non-stochastic Control](https://mlsanity.com/paper/2310.02261/) (2023)
- [Optimistic Online Non-stochastic Control via FTRL](https://mlsanity.com/paper/2404.03309/) (2024)
- [Safe and Efficient Online Convex Optimization with Linear Budget Constraints and Partial Feedback](https://mlsanity.com/paper/2412.03983/) (2024)
- [Constrained Online Convex Optimization with Memory and Predictions](https://mlsanity.com/paper/2603.21375/) (2026)

## Abstract (arXiv)

This paper studies online nonstochastic control problems with adversarial and static constraints. We propose online nonstochastic control algorithms that achieve both sublinear regret and sublinear adversarial constraint violation while keeping static constraint violation minimal against the optimal constrained linear control policy in hindsight. To establish the results, we introduce an online convex optimization with memory framework under adversarial and static constraints, which serves as a subroutine for the constrained online nonstochastic control algorithms. This subroutine also achieves the state-of-the-art regret and constraint violation bounds for constrained online convex optimization problems, which is of independent interest. Our experiments demonstrate the proposed control algorithms are adaptive to adversarial constraints and achieve smaller cumulative costs and violations. Moreover, our algorithms are less conservative and achieve significantly smaller cumulative costs than the state-of-the-art algorithm.