Active-Acquisition Evapotranspiration Inference for Computer Agriculture Irrigation Scheduling Under Sparse Sensor Placement: A Regret-Bound Evaluation

Sparse sensor placement in irrigation scheduling forces a choice between the cost of additional evapotranspiration (ET) observations and the regret incurred when a scheduling policy acts on an imprecise ET estimate. the present analysis formalises that choice as an active-acquisition problem in which a learner selects, at each decision epoch, whether to sample a costly ET reference or to act on the current posterior, and it derives a regret bound for the resulting policy under sub-Gaussian noise and a Lipschitz yield-loss function. The analysis separates the statistical error of ET inference from the agronomic cost of scheduling error, and it shows that the regret of the active policy decomposes into an acquisition term that scales with the square root of the number of reference samples and an information term governed by the mutual information between the sampled location and the field-mean ET. A bound is obtained that is tighter than the passive-sampling benchmark whenever the acquisition cost is below a threshold that depends on the Lipschitz constant of the yield-loss function and the conditional variance of ET given the sensor readings. The framework is illustrated with a reanalysis of monthly air temperature at Accra, Ghana, for 2000 to 2023 (312 monthly observations, mean 26.521 C, standard deviation 1.24 C, warming trend 0.1622 C per decade), which supplies the climatological prior against which the acquisition schedule is calibrated. The contribution is a regret bound that makes the trade-off between sensor cost and scheduling loss explicit and computable, and that identifies the conditions under which active acquisition is preferable to denser static instrumentation.