We revisit the so-called sampling and discarding approach used to quantify the probability of violation of a scenario solution when some of the original samples are allowed to be discarded. We propose a scheme that consists of a cascade of optimization problems, where at each step we remove a superset of the active constraints. By relying on results from compression learning theory, we produce a tighter bound for the probability of violation of the obtained solution than existing state-of-the-art one. Besides, we show that the proposed bound is tight by exhibiting a class of optimization problems that achieves the given upper bound. The improvement of the proposed methodology with respect to a scenario discarding scheme based on a greedy removal strategy is shown by means of an analytic example and a resource sharing linear program.
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