Genetic and drug perturbation screens are important tools for elucidating disease mechanisms and validating therapeutic targets, but experimental costs limit the number of candidates that can be tested. Existing perturbation screening methods typically update the surrogate model with feedback while keeping the acquisition function fixed, limiting their ability to adapt selection to different response landscapes. Experimental feedback reveals current hits and informs subsequent selection by updating candidate predictions, providing a training signal for learning how to select experiments. We formulate budgeted perturbation discovery as a sequential decision problem and propose Temporal Difference Active Learning (TDAL), which learns an acquisition function online through temporal difference learning from a single screening trajectory, accounting for current hits and future discoveries. TDAL uses the Hellinger distance between hit probabilities for unmeasured candidates before and after an experiment to weight successor value, and reuses measured outcomes through leave-batch-out (LBO) to construct virtual transitions and alleviate training data scarcity. Across eight public screens spanning single, double, and triple perturbations under varied experimental configurations, TDAL achieves an average rank of 1.63 among eleven methods and ranks first on four tasks, demonstrating its adaptability across response landscapes.

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