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Learning low-degree functions from a logarithmic number of random queries (2109.10162v3)
Published 21 Sep 2021 in cs.LG, math.FA, and stat.ML
Abstract: We prove that every bounded function $f:{-1,1}n\to[-1,1]$ of degree at most $d$ can be learned with $L_2$-accuracy $\varepsilon$ and confidence $1-\delta$ from $\log(\tfrac{n}{\delta})\,\varepsilon{-d-1} C{d{3/2}\sqrt{\log d}}$ random queries, where $C>1$ is a universal finite constant.