Myopic Experiment Selection Provably Cannot Do Science: A Proof That Information-Gain Planners Never Build the Instrument They Need

arXiv 2608.05085·low signalXBlueskyLinkedInCopy link

Automated discovery systems typically pick the next experiment by maximizing expected information gain per unit cost or a learned plausibility score. The paper identifies a structural failure: constructive actions that acquire an epistemic capability — an instrument, assay, pipeline, simulator, or abstraction — return no information inside a bounded horizon and are therefore dominated by any measurement with positive information, however small. Formulating goal-directed discovery as a stochastic shortest-path problem in belief space where constructive experiments change the downstream action graph, they prove that for every lookahead depth d there exists an instance where every myopic information-maximizing planner has an unbounded approximation ratio, and a related instance where it never reaches the goal at all; a controlled testbed shows the gap appearing only under capability-gating and persisting across all fixed horizons.