Learning convex bodies is hard

Details Learning convex bodies is hard Learning convex bodies is hard

2009-04-07

arxiv.org/abs/0904.1227v1

Computer Science

Learning

Scientific paper

We show that learning a convex body in $\RR^d$, given random samples from the body, requires $2^{\Omega(\sqrt{d/\eps})}$ samples. By learning a convex body we mean finding a set having at most $\eps$ 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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