2021
DOI: 10.48550/arxiv.2102.10199
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Information-Theoretic Bounds for Integral Estimation

Abstract: In this paper, we consider a zero-order stochastic oracle model of estimating definite integrals. In this model, integral estimation methods may query an oracle function for a fixed number of noisy values of the integrand function and use these values to produce an estimate of the integral. We first show that the informationtheoretic error lower bound for estimating the integral of a d-dimensional function over a region with l ∞ radius r using at most T queries to the oracle function is Ω 2 d r d+1 d/T . Addit… Show more

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