… , 𝑥𝑛 drawn i.i.d. from 𝑃𝑋 . ⊚ Generate 𝑛 random variables 𝜎1, … , 𝜎𝑛 ∈ {−1, +1}. Definition (Rademacher complexity) For a set of real-valued functions F with input space X, a distribution 𝑃𝑋 on X, and sample size 𝑛, the Rademacher complexity 𝑅(F, X, 𝑃𝑋 , 𝑛) is 𝑅(F, X, 𝑃𝑋 , 𝑛) = 𝔼 𝑥1 ,…,𝑥𝑛 ∼𝑃𝑋 𝜎1 ,…,𝜎𝑛 ∼𝐵𝑒𝑟(1/2) [sup 𝑓 ∈F | 2 𝑛 𝑛 ∑ 𝑖=1 𝜎𝑖 𝑓 (𝑥𝑖 )|] , (1) where 𝜎1 … , 𝜎𝑛 ∼ 𝐵𝑒𝑟(1/2) with values ±1. 5 ʢ 23