To achieve robustness to adaptive adversaries, Bernoulli and reservoir sampling require sample size Ω(log |R| / ε²) instead of the static VC-dimension bound.
Duffield, Haim Kaplan, Carsten Lund, and Mikkel Thorup
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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.