Lower bounds for the number of random bits in Monte Carlo algorithms

12/23/2020

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by   Stefan Heinrich, et al.

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We continue the study of restricted Monte Carlo algorithms in a general setting. Here we show a lower bound for minimal errors in the setting with finite restriction in terms of deterministic minimal errors. This generalizes a result of Heinrich, Novak, and Pfeiffer, 2004 to the adaptive setting. As a consequence, the lower bounds on the number of random bits from that paper also hold in this setting. We also derive a lower bound on the number of needed bits for integration of Lipschitz functions over the Wiener space, complementing a result of Giles, Hefter, Mayer, and Ritter, arXiv:1808.10623.