We show that learning a convex body in R d, given random samples from the body, requires 2 Ω( √ d/ǫ) samples. By learning a convex body we mean finding a set having at most ǫ relative symmetric difference with the input body. To prove the lower bound we construct a hard to learn family of convex bodies. Our construction of this family is very simple and based on error correcting codes.
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