Temporal-Difference Causal Inference for Computer Agriculture Fertilizer Response Under Anticipatory Farmer Behavior: An Artificial Intelligence Regret-Bound Evaluation

Fertilizer recommendation systems in computer agriculture typically treat farmer behaviour as an exogenous covariate, yet farmers anticipate the recommendations they receive and adjust their application rates before the season begins. the present analysis formalises that anticipatory feedback as a temporal-difference causal problem and derives a regret bound for an artificial-intelligence recommendation policy that must learn the fertilizer response function while the farmer's behaviour responds to the policy itself. The analysis is theoretical and design-based: no observational data are used or claimed. The operating characteristics of a before-after-control-impact estimator are characterised under a declared variance structure with between-cluster SD = 6.0, residual SD = 4.5 and intraclass correlation = 0.64, using 2000 replications per design cell across cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points. The design yields 54 clusters for 5 percentage points at 80% power. The bound implies that recommendation policies which ignore anticipation incur a regret floor that additional clusters cannot remove, and that the before-after-control-impact design identifies the response function only when the anticipatory shift is bounded. The conclusion is a design rule: anticipatory behaviour must be modelled as part of the causal estimand, not as a nuisance to be averaged away.