Certifying the Information Value of Adaptive Tool Use

An early network alarm can guide a tool-using agent’s next query. Yet when an interactive agent outperforms one that chooses all queries in advance, the gain may reflect better information, easier sequential processing, or additional inference compute. We define adaptive information value as the improvement in optimal expected task utility from choosing queries based on previous responses rather than fixing them in advance, under the same task and query budget. We derive a sound finite-budget certificate that upper-bounds optimal adaptive performance without enumerating adaptive policies. The certificate combines pairwise response-channel overlap with utility-sensitive fractional matching and supports arbitrary finite priors and utilities, heterogeneous query costs, multivalued responses, and memoryless noise. Controlled network-diagnosis experiments show that changing only the tool interface can create or eliminate adaptive information value. Across 63 selected topology lineages and three language-model families, externally optimized adaptive evidence improves prediction accuracy by 5.84 percentage points on the positive-gap interface, with a 4.37-point larger gain than on a matched zero-gap control; both effects remain significant after Holm correction. However, when the models select their own queries, adaptive querying underperforms pre-committed querying in our tests, distinguishing the ability to use adaptive evidence from the ability to select it. Our framework provides a benchmark-level audit of whether feedback creates an information advantage before attributing multi-turn gains to adaptive acquisition.