Pre-Disclosure Experiment Menus: Oracle-Relative Risk and Joint Sample--Menu Asymptotics

What the math gives to ML

The paper converts a pre-disclosure experiment-menu problem into a task-aware minimax quantization problem. Its transferable asset is the explicit distortion between an oracle action and a restricted action, weighted by target sensitivity and inverse Fisher information, together with the rate law A_k proportional to k^(-2/r) on a uniformly quadratic r-dimensional oracle image. A neural analogue is to replace a large family of context-dependent experts or low-rank adapters by a finite menu selected before inference, while a router chooses among the retained entries after seeing the input. This gives a principled alternative to parameter-space clustering and predicts how accuracy should degrade as the menu size shrinks.