# Online Optimal Control with Affine Constraints

arXiv: https://arxiv.org/abs/2010.04891 · HTML: https://mlsanity.com/paper/2010.04891/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Oct 2020.

## Built on by (most cited first, 20 of 20)

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- [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)
- [Online Nonstochastic Control with Adversarial and Static Constraints](https://mlsanity.com/paper/2302.02426/) (2023)
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- [RASteer: Retain-Aware Activation Steering for Concept Erasure in Diffusion Models](https://mlsanity.com/paper/2610.01969/) (2026)
- [Regret Analysis of Policy Optimization over Submanifolds for Linearly Constrained Online LQG](https://mlsanity.com/paper/2403.08553/) (2024)
- [Constrained Online Convex Optimization with Memory and Predictions](https://mlsanity.com/paper/2603.21375/) (2026)
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- [Continual Concept Erasure in Diffusion Models by Suppressing Cross-Edit Interference](https://mlsanity.com/paper/2610.01989/) (2026)

## Abstract (arXiv)

This paper considers online optimal control with affine constraints on the states and actions under linear dynamics with bounded random disturbances. The system dynamics and constraints are assumed to be known and time-invariant but the convex stage cost functions change adversarially. To solve this problem, we propose Online Gradient Descent with Buffer Zones (OGD-BZ). Theoretically, we show that OGD-BZ with proper parameters can guarantee the system to satisfy all the constraints despite any admissible disturbances. Further, we investigate the policy regret of OGD-BZ, which compares OGD-BZ's performance with the performance of the optimal linear policy in hindsight. We show that OGD-BZ can achieve a policy regret upper bound that is the square root of the horizon length multiplied by some logarithmic terms of the horizon length under proper algorithm parameters.