# Safe Control with Minimal Regret

arXiv: https://arxiv.org/abs/2203.00358 · HTML: https://mlsanity.com/paper/2203.00358/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Mar 2022.

## Built on by (most cited first, 7 of 7)

- [Implications of Regret on Stability of Linear Dynamical Systems](https://mlsanity.com/paper/2211.07411/) (2022)
- [A Distributionally Robust Approach to Regret Optimal Control using the Wasserstein Distance](https://mlsanity.com/paper/2304.06783/) (2023)
- [Optimal Competitive-Ratio Control](https://mlsanity.com/paper/2206.01782/) (2022)
- [Regret Analysis of Online Gradient Descent-based Iterative Learning Control with Model Mismatch](https://mlsanity.com/paper/2204.04722/) (2022)
- [Constrained Online Decision-Making: A Unified Framework](https://mlsanity.com/paper/2505.07101/) (2025)
- [Follow the Clairvoyant: an Imitation Learning Approach to Optimal Control](https://mlsanity.com/paper/2211.07389/) (2022)
- [Distributionally Robust Regret Optimal Control Under Moment-Based Ambiguity Sets](https://mlsanity.com/paper/2512.10906/) (2025)

## Abstract (arXiv)

As we move towards safety-critical cyber-physical systems that operate in non-stationary and uncertain environments, it becomes crucial to close the gap between classical optimal control algorithms and adaptive learning-based methods. In this paper, we present an efficient optimization-based approach for computing a finite-horizon robustly safe control policy that minimizes dynamic regret, in the sense of the loss relative to the optimal sequence of control actions selected in hindsight by a clairvoyant controller. By leveraging the system level synthesis framework (SLS), our method extends recent results on regret minimization for the linear quadratic regulator to optimal control subject to hard safety constraints, and allows competing against a safety-aware clairvoyant policy with minor modifications. Numerical experiments confirm superior performance with respect to finite-horizon constrained H2 and H_∞ control laws when the disturbance realizations poorly fit classical assumptions.