Active Calibration of Reachable Sets Using Approximate Pick-to-Learn
This addresses the challenge of efficient calibration for safety-critical systems like robotics, though it is incremental as it adapts existing methods to a specific setting.
The paper tackles the problem of costly calibration for reachable sets in learned models by proposing an active learning strategy that adapts the Pick-to-Learn algorithm to produce probabilistic guarantees, requiring fewer samples and providing more accurate sets than baselines in a simulated drone racing example.
Reachability computations that rely on learned or estimated models require calibration in order to uphold confidence about their guarantees. Calibration generally involves sampling scenarios inside the reachable set. However, producing reasonable probabilistic guarantees may require many samples, which can be costly. To remedy this, we propose that calibration of reachable sets be performed using active learning strategies. In order to produce a probabilistic guarantee on the active learning, we adapt the Pick-to-Learn algorithm, which produces generalization bounds for standard supervised learning, to the active learning setting. Our method, Approximate Pick-to-Learn, treats the process of choosing data samples as maximizing an approximate error function. We can then use conformal prediction to ensure that the approximate error is close to the true model error. We demonstrate our technique for a simulated drone racing example in which learning is used to provide an initial guess of the reachable tube. Our method requires fewer samples to calibrate the model and provides more accurate sets than the baselines. We simultaneously provide tight generalization bounds.