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We establish a tight characterization of the worst-case rates for the excessrisk of agnostic learning with sample compression schemes and for uniformconvergence for agnostic sample compression schemes. In particular, we findthat the optimal rates of convergence for size-$k$ agnostic sample compressionschemes are of the form $\sqrt{\frac{k \log(n/k)}{n}}$, which contrasts withagnostic learning with classes of VC dimension $k$, where the optimal rates areof the form $\sqrt{\frac{k}{n}}$.

A New Lower Bound for Agnostic Learning with Sample Compression Schemes