Sample-Efficient Optimization over Generative Priors via Coarse Learnability

We study zeroth-order optimization where solutions must minimize a cost $d(s)$ while maintaining high probability under a complex generative prior $L(s)$ (e.g., a parameterized model). This reduces to sampling from a target distribution proportional to $L(s) e^{-T \cdot d(s)}$. Since classical model