# When Can Safe Controllers Adapt? Information before Commitment

arXiv: https://arxiv.org/abs/2607.16895 · HTML: https://mlsanity.com/paper/2607.16895/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 41 references that are in the map.
- First posted on arXiv 18 Jul 2026.

## Builds on (most cited first, 17 of 17)

- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [Safe Model-based Reinforcement Learning with Stability Guarantees](https://mlsanity.com/paper/1705.08551/) (2017)
- [A General Safety Framework for Learning-Based Control in Uncertain Robotic Systems](https://mlsanity.com/paper/1705.01292/) (2017)
- [On the Sample Complexity of the Linear Quadratic Regulator](https://mlsanity.com/paper/1710.01688/) (2017)
- [A predictive safety filter for learning-based control of constrained nonlinear dynamical systems](https://mlsanity.com/paper/1812.05506/) (2018)
- [Naive Exploration is Optimal for Online LQR](https://mlsanity.com/paper/2001.09576/) (2020)
- [Linear Stochastic Bandits Under Safety Constraints](https://mlsanity.com/paper/1908.05814/) (2019)
- [Safe Exploration in Finite Markov Decision Processes with Gaussian Processes](https://mlsanity.com/paper/1606.04753/) (2016)
- [Learning Linear-Quadratic Regulators Efficiently with only √T Regret](https://mlsanity.com/paper/1902.06223/) (2019)
- [Safely Learning to Control the Constrained Linear Quadratic Regulator](https://mlsanity.com/paper/1809.10121/) (2018)
- [Data informativity: a new perspective on data-driven analysis and control](https://mlsanity.com/paper/1908.00468/) (2019)
- [Learning-based Model Predictive Control for Safe Exploration and Reinforcement Learning](https://mlsanity.com/paper/1906.12189/) (2019)
- [Safe Linear Bandits over Unknown Polytopes](https://mlsanity.com/paper/2209.13694/) (2022)
- [Safe Adaptive Learning-based Control for Constrained Linear Quadratic Regulators with Regret Guarantees](https://mlsanity.com/paper/2111.00411/) (2021)
- [Foundations of Safe Online Reinforcement Learning in the Linear Quadratic Regulator: √T-Regret](https://mlsanity.com/paper/2504.18657/) (2025)
- [Rate-Optimal Regret for the Safe Learning-based Control of the Constrained Linear Quadratic Regulator](https://mlsanity.com/paper/2604.22158/) (2026)

## Abstract (arXiv)

Safe adaptive control is online adaptation under a safety guarantee on the learning trajectory itself. The controller may use any causal, history-dependent rule and act differently across environments as data arrive. Only its safety guarantee is uniform: the same rule must satisfy it under every initially plausible model. Performance is measured against a safe oracle that knows the realized model. Many finite-time analyses assume persistent excitation of the uniformly safe closed loop, so the data distinguish every pair of models requiring different control decisions. Under that assumption, feasibility is already settled; only the rate remains. We ask instead: Do the safety constraints permit such an informative experiment at all? While an alternative remains plausible, the controller must preserve a safe continuation under it. We call the first action that forecloses such a continuation commitment. Chance safety allows commitment only on an event rare under the alternative, and the evidence must arrive beforehand: the observation generated by the committing action is too late. We define precommitment information as the KL divergence between learner-visible laws stopped before commitment. Our main result is a causal reduction. The commitment rule determines (1) the probability that safety permits commitment under the alternative, (2) the target-side cost of remaining noncommittal, (3) and the information available when the decision is made. Bounded precommitment information therefore leaves a fixed fraction of the oracle gap unavoidable. If the gap is Omega(T), every uniformly safe policy has linear regret. We establish the obstruction in a constrained linear system with quadratic regulation cost. We also prove recovery in special cases and derive semidefinite upper certificates for deterministic linear-Gaussian systems.