Privacy-Budget Evaluation for Computer Agriculture Federated Pest-Outbreak Detection Under Cross-Farm Sample Heterogeneity: An Artificial Intelligence Differential-Privacy Utility Bound

Federated learning allows farms to train a shared pest-outbreak detector without pooling raw scouting records, but the differential-privacy noise added to protect each farm's updates degrades detection utility in ways that depend on how heterogeneous the farms are. The bound is derived from a Rényi-differential-privacy accountant combined with a PAC-Bayes generalisation term that carries an explicit cross-farm heterogeneity penalty. The analysis yields a closed-form expression linking the privacy budget, the number of participating farms, the heterogeneity measured by a Wasserstein distance between farm distributions, and the achievable balanced accuracy of the federated detector. The bound predicts that the utility cost of a fixed privacy budget grows with heterogeneity, so that a budget adequate for homogeneous farms is insufficient when prevalence varies across farms. The result is a design rule for setting the privacy budget in agricultural federated learning and a benchmark against which empirical privacy-utility curves can be evaluated. The contribution is a formal, heterogeneity-aware utility bound rather than an empirical measurement, and it is stated as a proposition with explicit assumptions and boundary conditions.