Weighting function for Non Uniform Learning

Consider a hypothesis class $$H = \cup_{n=1}^{\infty} H_n$$, where for every $$n\in N$$, $$H_n$$ is finite. Find a weighting function $$w : H ->[0, 1]$$ such that $$\sum_{h \in H} w(h) ≤ 1$$ and so that for all $$h \in H$$, $$w(h)$$ is determined by $$n(h) = min\{n :h \in H_n\}$$ and by $$|H_n(h)|$$.
Since every $$H_n$$ is finite, it is agnostic PAC learnable. And hence their union $$H$$ is non-uniform learnable. However I am unable to proceed from here.

1 Answer

For every $$n\in \mathbb{N}$$, and $$h\in H_n$$, we can use $$w(h)$$ = $$\frac{2^{−n}}{|H_n|}$$.