Property 2: Jensen Gap

Watch the gap between the Bernstein Operator and the convex cost function as the sample size grows.

Sample size — k Bernoulli(0.5) trials 6

f(x) = x⁴ sampling dist. of mean (k trials) f(0.5) = 0.0625 E[f(X̄ₖ)]

f(mean) = f(0.5)

0.0625

E[f(X̄ₖ)] = Bernₖ(f)(0.5)

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Jensen gap

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