Opportunity Is Not Realizability: Selection-Valid Diagnostics for Multi-LLM Routing
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Computer Science > Machine Learning
Title:Opportunity Is Not Realizability: Selection-Valid Diagnostics for Multi-LLM Routing
Abstract:Oracle routing measures how much a pool of language models could gain from per-query selection, but the diagnostic has two flaws: testing against a best fixed model selected on the same examples invalidates paired inference, and a full-information oracle sees outcomes no deployable router observes. We separate three estimands (outcome-oracle opportunity, the Bayes-optimal gain from a declared pre-answer signal, and the held-out gain of a learned router) and prove selection-valid confidence intervals that survive choosing the best fixed model or the best member of a router family, a signal-information sandwich, and a $(1-1/e)$ greedy guarantee for building compact pools from submodular complementary coverage. On eight checkpoints from six families over four benchmarks, selection-valid intervals certify a population oracle gap of $9.7$--$30.7$ points on every task, yet the strongest deployable prompt router recovers only $7.5$--$14.4\%$ of it, and the simultaneous interval for the best of eleven tested policies has lower limit zero throughout. The realizable share of oracle opportunity is small and certifiable: strong routers beat the best fixed model, and most of the gap remains.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2608.08265 [cs.LG] |
| (or arXiv:2608.08265v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2608.08265
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