Corollary 13.7: for a β-smooth nonnegative loss and λ ≥ 2β/m, RLM satisfies E[ℓ(A(S⁽ⁱ⁾), zᵢ) − ℓ(A(S), zᵢ)] ≤ (48β/(λm)) E[L_S(A(S))], and ≤ 48βC/(λm) if ℓ(0, z) ≤ C

Initializing...

Corollary 13.7: for a β-smooth nonnegative loss and λ ≥ 2β/m, RLM satisfies E[ℓ(A(S⁽ⁱ⁾), zᵢ) − ℓ(A(S), zᵢ)] ≤ (48β/(λm)) E[L_S(A(S))], and ≤ 48βC/(λm) if ℓ(0, z) ≤ C · Prove2Me