Detecting an Effect Is Not Learning to Act on It: A Reward-SNR Floor for LLM Acquisition Agents

Abstract

Many pipelines can pay a per-example cost to acquire an auxiliary, model-derived observation -- an LLM's structured reasoning, a slow oracle, an expensive measurement -- and then must decide when the acquired signal is worth using. Our thesis is a distinction that is easy to miss: detecting that such a signal helps on average is not the same as learning to act on it per instance, and a reward-SNR floor governs when the second is even possible. Even when the signal is faithful and an in-sample oracle picking the top-b examples by realized reward shows a sizable apparent gain, no deployable policy can learn when to acquire it: across per-impression, cluster, regime, and uplift-tree granularities, learned routing never beats random, and a matched-moment noise placebo reproduces>=100% of the oracle's apparent gain -- the apparent"learnable structure"is order statistics of noise. We explain this with one distinction, detecting a mean effect vs. learning a per-instance acquisition policy, and a reward-SNR detectability floor: routing is estimable offline only if the reward SNR rho clears rho*(N) ~= 2.8/sqrt(N), with a positive control confirming a true low-SNR limit rather than a broken pipeline. As a concrete instantiation we introduce Structured Hypothesis Embeddings (SHE): a frozen LLM turns a user history into ranked, confidence-scored, evidence-grounded intent hypotheses, fused into a recommender. On three public datasets (MIND, REES46, Amazon-Beauty), SHE is faithful and calibratable, yet its value is backbone- and regime-conditional (significant over an ordered GRU, +0.0114, 95% CI [+0.0030, +0.0209], but a global redundancy gap indistinguishable from zero), and learned acquisition collapses at every granularity because all three datasets sit below the floor. The realizable unit is a design-time regime gate, not a per-instance policy. We release code and a one-command reproduction.