The gap between the expected (with respect to test distribution) loss R(h) and empirical risk L(h; λ, α) is bounded as |R(h) − L(h; λ, α)| ≤ Eptr pte(x) ptr(x) − w(α,λ)(x) ℓ(h(x, y(x))) +25/4 max Eptr (w(α,λ)(x))2ℓ2(h(x, y(x))), Eˆ ptr (w(α,λ)(x))2ℓ2(h(x, y(x)) × p log 2ntr p + log 4 δ ntr 3 8 . (5) In the above inequality, p is the pseudo-dimension of the function class. Masanari Kimura (SOKENDAI) IGIWERM January 6, 2024 22 / 26