Differentially-Private Federated Learning for Computer Agriculture Pest Inference Across Smallholder Smartphone Fleets Under Cross-Device Heterogeneity: An Artificial Intelligence Privacy-Utility Bound

Federated learning promises to train pest-inference models on smallholder smartphone fleets without centralising raw imagery, but the differential-privacy noise required to protect individual contributions interacts with cross-device heterogeneity in ways that existing privacy-utility analyses do not capture. The analysis derives a closed-form expression for the excess risk of the privatised federated estimator as a function of the privacy budget, the number of participating devices, the local sample size, and a heterogeneity coefficient that quantifies the dispersion of device-level data distributions. The bound shows that the utility cost of privacy is not monotone in fleet size: beyond a threshold determined by the heterogeneity coefficient, adding devices increases the bias contribution faster than it reduces the variance contribution, so that privacy and heterogeneity compound rather than offset. A corollary establishes that clipping norm and noise scale must be co-tuned to the heterogeneity coefficient, and that the standard practice of fixing the clipping norm across devices is suboptimal when heterogeneity is high. The bound is stated for the convex smooth setting and its extension to the non-convex stochastic setting is discussed. The contribution is a device-heterogeneity-aware privacy-utility characterisation that reframes the design of differentially-private federated learning for agricultural pest inference as a joint tuning problem over privacy, fleet composition, and local data dispersion.