Counterfactual Field Layout Learning for Artificial Intelligence Agriculture Variable-Rate Seeding Under Unobserved Soil Heterogeneity: A Computer Policy-Regret Evaluation

Variable-rate seeding (VRS) promises yield gains by matching plant density to soil productivity, but the soil maps that would justify prescription are almost never observed at the within-field resolution the machinery requires. the present analysis formalises VRS prescription as a counterfactual field-layout learning problem in which the decision-maker must choose a seeding prescription from a finite library using only covariates and logged yield, while the latent productivity surface remains unobserved. A policy-regret framework is developed that separates the regret attributable to model misspecification from the regret attributable to the information limit imposed by unobserved heterogeneity, and a doubly-robust counterfactual risk estimator is proposed whose bias is bounded under overlap and bounded conditional outcome variance. The analysis is methodological and theoretical: no field trial was conducted and no empirical estimate is reported. The framework yields three results. First, the regret of any prescription policy decomposes into an approximation term that shrinks with library richness and an identification term that does not, so that enriching the prescription library beyond the resolution of the covariate signal cannot reduce regret. Second, the doubly-robust estimator is consistent for the counterfactual seeding risk when either the propensity of the logged layout or the outcome model is correctly specified, and its finite-sample bias is bounded by a term proportional to the overlap deficiency of the logging policy. Third, a policy-regret lower bound is derived showing that under unobserved soil heterogeneity the minimax regret is bounded away from zero by a quantity proportional to the conditional variance of the latent productivity surface given the covariates. VRS evaluation should report regret against the achievable information limit rather than against the observed-yield benchmark, and it specifies the logging and overlap conditions under which such an evaluation is identifiable.