When Can Safe Controllers Adapt? Information before Commitment
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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.
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References · 17
- 2019Control Barrier Functions: Theory and Applicationscited by 372
- 2021Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learningcited by 371
- 2017Safe Model-based Reinforcement Learning with Stability Guaranteescited by 366
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- 2018A predictive safety filter for learning-based control of constrained nonlinear dynamical systemscited by 118
- 2020Naive Exploration is Optimal for Online LQRcited by 116
- 2019Linear Stochastic Bandits Under Safety Constraintscited by 90
- 2016Safe Exploration in Finite Markov Decision Processes with Gaussian Processescited by 75
- 2019Learning Linear-Quadratic Regulators Efficiently with only √T Regretcited by 70
- 2018Safely Learning to Control the Constrained Linear Quadratic Regulatorcited by 33
- 2019Data informativity: a new perspective on data-driven analysis and controlcited by 19
5 more
- 2019Learning-based Model Predictive Control for Safe Exploration and Reinforcement Learningcited by 16
- 2022Safe Linear Bandits over Unknown Polytopescited by 14
- 2021Safe Adaptive Learning-based Control for Constrained Linear Quadratic Regulators with Regret Guaranteescited by 11
- 2025Foundations of Safe Online Reinforcement Learning in the Linear Quadratic Regulator: √T-Regretcited by 2
- 2026Rate-Optimal Regret for the Safe Learning-based Control of the Constrained Linear Quadratic Regulatorcited by 1
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