To achieve robustness to adaptive adversaries, Bernoulli and reservoir sampling require sample size Ω(log |R| / ε²) instead of the static VC-dimension bound.
Gilbert, Brett Hemenway, Martin J
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The Adversarial Robustness of Sampling
To achieve robustness to adaptive adversaries, Bernoulli and reservoir sampling require sample size Ω(log |R| / ε²) instead of the static VC-dimension bound.