Sparse-Reward Exploration for Artificial Intelligence Agriculture Robotic Weeding Under Delayed Crop-Injury Signals: A Computer Sample-Complexity Regret Bound

Robotic weeding systems that learn from delayed crop-injury signals face a sample-complexity problem that standard multi-armed bandit theory does not address: the reward is sparse, the injury signal arrives several decision epochs after the action, and the exploration policy must trade off weed removal against crop damage under a fixed budget of field trials. The algorithm maintains optimistic action-value estimates under a delay-augmented confidence set and selects actions by an upper-confidence rule that inflates with the observed delay. The main result is a sample-complexity regret bound of order O(sqrt(K T log T) + K D log T), where K is the number of weed-management actions, T is the horizon, and D is the maximum delay in epochs. The bound is derived under a sub-Gaussian noise assumption and a bounded crop-injury penalty, and it is shown to be tight up to logarithmic factors via a matching lower bound. A secondary contribution is a delay-aware exploration rate that reduces the effective sample complexity by a factor proportional to the inverse of the delay when the delay distribution is known. The analysis is theoretical: no field data are used or claimed. The bound provides a design target for practitioners specifying how many weeding trials a robotic system must run before its crop-injury rate stabilises, and it clarifies why naive optimistic exploration fails when the injury signal is delayed.