Benchmarking Evaluation of Differentially Private Federated Learning for Computer Agriculture Disease Classifiers Under Cross-Farm Privacy Budgets: An Artificial Intelligence Utility-Loss Bound for Smallholder Participation

Differentially private federated learning (DP-FL) promises to let smallholder farms contribute to crop-disease classifiers without surrendering raw imagery, but the utility cost of the privacy budget is usually reported for a single farm or a single model, not for the cross-farm budgets that a real cooperative would have to negotiate. The framework formalises the cross-farm budget allocation as a constrained optimisation over per-farm noise scales, states a utility-loss bound in terms of the number of participating farms, the per-farm budget and the heterogeneity of local label distributions, and specifies a benchmarking protocol that reports accuracy, macro-F1 and participation cost against the bound. No observational data are used or claimed: the analysis characterises the operating characteristics of the design under a declared variance structure (between-cluster SD = 6.0, residual SD = 4.5, intraclass correlation = 0.640), with power estimated across 2000 design cells. The computed intraclass correlation of 0.64 implies that farm-level clustering dominates the variance and that the effective sample size for a cross-farm benchmark is far below the nominal farm count. The bound predicts that the marginal utility of admitting an additional farm falls sharply once the per-farm budget drops below a threshold that depends on label heterogeneity, which reframes smallholder participation as a budget-allocation problem rather than a data-volume problem. The contribution is a formal, testable statement of the utility-loss trade-off that a computer-agriculture benchmark can evaluate without access to protected farm data.