Federated Inference for Computer Agriculture Pest-Risk Prediction Under Cross-Farm Non-IID Data: An Artificial Intelligence Differential-Privacy Utility Bound

Pest-risk prediction across federated farms is complicated by heterogeneity in local data distributions and by the privacy guarantees required for sharing model updates. The analysis formalises the federated learning problem as minimising a weighted sum of local empirical risks subject to a Rényi differential privacy constraint, and derives a high-probability bound on the excess risk of the private federated estimator relative to the non-private oracle. The bound decomposes into three terms: a statistical term that scales with the number of farms and local sample sizes, a heterogeneity term that depends on the divergence between local and global risk minimisers, and a privacy term that grows with the noise multiplier and the number of inference rounds. The principal result shows that the privacy-utility trade-off is governed by the product of the noise multiplier and the square root of the number of rounds, and that this product can be controlled by early stopping without sacrificing the statistical rate. The bound is illustrated through a design-based evaluation using a before-after-control-impact estimator with an intraclass correlation of 0.64, between-cluster standard deviation of 6.0 and residual standard deviation of 4.5; power was estimated across 2000 replications per cell for cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points. The results indicate that 54 clusters are required for 80% power at a 5 percentage point effect. The paper concludes that differential privacy in federated pest-risk prediction imposes a quantifiable and manageable cost, and that the bound provides a principled basis for selecting privacy parameters in agricultural inference systems.