A.2 Self-consistentequationsfortheexcesspredictionerror Definingz =n

Therefore, strictly speaking the results derived hereafter are not rigorous, and we assume that the typical excess error can still be computed from eq.(27). In fact, this is well-justified by comparing the results obtained from extrapolating the theory withfinite instance simulation,e.g. Note that the scalings ofz with respect ton differ according to the regularisationλ, depending on which of the two terms on the right hand side of equation(37) dominates. If the firstnλ term dominates, then(37) simplifies to z nλ. In the converse case where the second term in(37) dominates, z n1 α.