Let $f,f_i:[0,1]^d\rightarrow \mathbb{R}^k$ be continuous functions. Suppose that there are regions $\Omega_i \subset [0,1]^d$ (Compact) such that $f=\sum_i f_i 1_{\Omega_i}$. Is there a learning algorithm (with proven consistency properties) which selects the optimal $\Omega_i$?
Here, say $k$ is fixed.