Abstract
We study learning problems in which the underlying class is a bounded subset of L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> and the target Y belongs to L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> . Previously, minimax sample complexity estimates were known under such boundedness assumptions only when p=∞. We present a sharp sample complexity estimate that holds for any p > 4; it is based on a learning procedure that is suited for heavy-tailed problems.
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