Learning low-degree functions from a logarithmic number of random queries

TL;DR

This paper demonstrates that low-degree bounded functions over the hypercube can be efficiently learned with a logarithmic number of random queries, providing bounds on the sample complexity based on degree and accuracy.

Contribution

It establishes a new bound on the number of random queries needed to learn bounded low-degree functions with specified accuracy and confidence.

Findings

Learning complexity depends logarithmically on n and polynomially on 1/ε.

Achieves learning with a number of queries exponential in d^{3/2}√log d.

Provides a universal bound involving a constant C for all degrees d.

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.