Decision-Sensitive Compression with Learned Actuation

A compressed predictor can support accurate decisions without predicting every output accurately. This is harder to certify when the action response is also learned: a full-matrix error bound includes irrelevant output noise. We develop a finite-sample alternative for quadratic decisions. A Gaussian expansion at the fixed true optimal controller, together with calibrated low-dimensional moments, bounds the first-order decision error without a leading factor proportional to the square root of the output dimension; noise products and the plug-in Gram bias remain explicit. The resulting observable policy ball certifies arbitrary fitted linear controllers, and its optimal rank-constrained controller is ordinary plug-in compression. A local-rotation lower bound isolates the gap-dependent difficulty of selecting a representation, while a task-sampling bound separates physical calibration from generalization to fresh objectives. Experiments test irrelevant outputs, observable gap resolution, sampled tasks, and neural nuisance–capacity tradeoffs with learned actuation. Calibration improves markedly in the many-output regime, but remains conservative and is not uniformly tighter at small sample sizes. The analysis does not certify nonlinear pilots or closed-loop latent world models.