Cost-Weighted Neyman Allocation

The cost-weighted Neyman allocator is interpreted as the quality lever because it concentrates rollouts on high-variance, lower-cost prompts. The formal theorem gives a unique variance-minimizing continuous allocation under a token budget. The allocation rule minimizes trace variance of the policy-gradient estimator under a token budget. The cost-weighted Neyman optimum assigns more rollouts to prompts with higher within-prompt gradient variance and favors shorter prompts through expected length. DUET uses a running per-prompt surrogate because true prompt variance is unavailable before generation.