For real-time services, such as VoIP and videoconferencing supplied through a multi-domain MPLS network, it is vital to guarantee end-to-end QoS of the inter-domain paths. Thus, it is important to allocate an appropriate QoS class to the inter-domain paths in each transit domain. Because each domain has its own policy for QoS class allocation, each domain must then allocate an appropriate QoS class adaptively based on the estimation of the QoS class allocation policies adopted in other domains. This paper proposes an adaptive method for acquiring a QoS class allocation policy through the use of reinforcement learning. This method learns the appropriate policy through experience in the actual QoS class allocation process. Thus, the method can adapt to a complex environment where the arrival of inter-domain path requests does not follow a simple Poisson process and where the various QoS class allocation policies are adopted in other domains. The proposed method updates the allocation policy whenever a QoS class is actually allocated to an inter-domain path. Moreover, some of the allocation policies often utilized in the real operational environment can be updated and refined more frequently. For these reasons, the proposed method is designed to adapt rapidly to variances in the surrounding environment. Simulation results verify that the proposed method can quickly adapt to variations in the arrival process of inter-domain path requests and the QoS class allocation policies in other domains.