An efficient synthesis technique for modern analog circuits is important yet challenging due to the repeatedly re-synthesis process. To precisely explore the analog circuit performance limitation on the required technology is time-consuming. This work presents a learning-based framework for searching the limitation of analog circuits. With hierarchical architecture, the dimension of solution space can be reduced. Bayesian linear regression and support vector machine model are selected to speed up the algorithm and better performance quality can be retrieved. Experimental results show that our approach on two analog circuits can achieve up to 9x runtime speed-up without surrendering performance qualities.