The growing complexity of networks and the variety of future scenarios with diverse and often stringent performance requirements call for a higher level of automation. Intent-based management emerges as a solution to attain high level of automation, enabling human operators to solely communicate with the network through high-level intents. The intents consist of the targets in the form of expectations (i.e., latency expectation) from a service and based on the expectations the required network configurations should be done accordingly. It is almost inevitable that when a network action is taken to fulfill one intent, it can cause negative impacts on the performance of another intent, which results in a conflict. In this paper, we aim to address the conflict issue and autonomous management of intent-based networking, and propose an online learning method based on the hierarchical multi-armed bandits approach for an effective management. Thanks to this hierarchical structure, it performs an efficient exploration and exploitation of network configurations with respect to the dynamic network conditions. We show that our algorithm is an effective approach regarding resource allocation and satisfaction of intent expectations.