When Can Safe Controllers Adapt? Information before Commitment
Machine Learning
Summary
The authors study how controllers can safely learn and adapt online without causing unsafe behavior, even when the true system model is initially unknown. They show that to make safe decisions that rule out alternative models (commitment), the controller needs enough early information, measured by a quantity called precommitment information. If this information is limited, the controller can’t avoid some amount of performance loss, meaning the learning process will have unavoidable regret over time. They prove this limitation using a math model and also find cases where the controller can recover, providing methods to check safety in specific linear systems.
Authors
Venkatesh Saligrama
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 Ω(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.