In this paper, an intelligent probing method for interference constraint learning is proposed to allow a centralized cognitive radio network (CRN) to access the frequency band of a primary user (PU) in an underlay cognitive communication scenario. The main idea is that the CRN probes the PU and subsequently eavesdrops the reverse PU link to acquire the binary ACK/NACK packet. This feedback is implicit channel state information of the PU link, indicating whether the probing-induced interference is harmful or not. The intelligence of this sequential probing process lies in the selection of the power levels of the secondary users, which aims to minimize the number of probing attempts, a clearly active learning (AL) procedure, and expectantly the overall PU QoS degradation. The enhancement introduced in this paper is that we incorporate the probability of each feedback being correct into this intelligent probing mechanism by using a multivariate Bayesian AL method. This technique is inspired by the probabilistic bisection algorithm and the deterministic cutting plane methods (CPMs). The optimality of this multivariate Bayesian AL method is proven and its effectiveness is demonstrated through numerical simulations. Computationally cheap CPM adaptations are also presented, which outperform existing AL methods.