Budget-Constrained Active Sensing for Artificial Intelligence Agriculture Soil Moisture Mapping Under Sensor Placement Uncertainty: A Computer Regret-Bound Evaluation

Active soil-moisture sensing for artificial-intelligence agriculture must decide where to place a fixed number of probes before the moisture field is known, and must do so while the placement itself perturbs the estimate that guides the next placement. the present analysis formalises that decision as a budget-constrained sequential design problem over a Gaussian-process surrogate of the moisture field, and derives a regret bound that separates the irreducible approximation error of the surrogate from the information cost of exploration. The bound is evaluated analytically rather than empirically: a before-after-control-impact design with between-cluster standard deviation 6.0, residual standard deviation 4.5 and intraclass correlation 0.64 is used to characterise the operating characteristics of the estimator under a declared variance structure, with power estimated across 2000 design cells. The regret of greedy information-gain placement is bounded by the posterior variance of the surrogate at the unsampled locations, and that this bound degrades gracefully as the intraclass correlation rises. The contribution is a design-time certificate: a practitioner can compute, before deploying any probe, whether a proposed budget is sufficient to guarantee a stated mapping accuracy, and can identify the cluster count at which further sensing yields no reduction in regret.