When Can Safe Controllers Adapt? Information before Commitment

Title:When Can Safe Controllers Adapt? Information before Commitment

Abstract: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.

Machine Learning (cs.LG); Systems and Control (eess.SY)

arXiv:2607.16895 [cs.LG]

(or arXiv:2607.16895v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2607.16895 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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