An Agnostic Sample Compression Scheme for Squared Loss of Near-Linear Size in the Fat-Shattering Dimension

We construct, for every function class $\mathcal{F}\subseteq[0,1]^{\mathcal{X}}$ and every accuracy $0<α\le 1$, an agnostic sample compression scheme for the empirical squared loss: for every finite sample $S\in(\mathcal{X}\times[0,1])^m$ with arbitrary (noisy) labels, the scheme stores at most $O(\