The Realizability Assumption
  • the assumption:
    • there exists β„Ž*∈𝐻 such that 𝐿(𝐷,𝑓)(β„Ž*) = 0
    • there exists β„Ž*∈𝐻 such that 𝐏π‘₯∼𝐷(β„Ž*(π‘₯) = 𝑓(π‘₯)) = 1
  • Note that this assumption implies that with probability 1 over random samples, 𝑆, where the instances of 𝑆 are sampled according to 𝐷 and are labeled by 𝑓, we have 𝐿𝑆(β„Ž*) = 0