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The convex hull of a set $X$ of points in a Euclidean space is the smallest convex set that contains $X$.
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Convex hull of piece-wise linear functions
Let $K>1$ be a positive integer. Consider a function class $$\mathcal{F}_K:=\Big\{\max_{1\leq k\leq K} a_k^\top x + b_k:\ ||a_k||\leq 1, |b_k|\leq 1, \forall 1\leq k\leq K \Big\}$$ on some compact reg …