Network bandwidth reservation is a representative service that utilizes the advantages of software-defined networks, such as flexibility, in which users directly reserve network resources on an on-demand basis. An instantaneous response to user requests (e.g., less than 1 s) and a high request acceptance ratio (e.g., over 90%) are required to provide bandwidth reservation services extensively. In this study, we propose a bandwidth reservation method to meet these two requirements by combining machine learning (ML) and linear programming (LP) technologies, particularly for unpredictable bandwidth demands that occur when an arbitrary user requires an infrequent or unexpected network bandwidth, in which the usage time is strictly indicated. In the proposed method, a user request is instantaneously and intuitively judged as accepted or rejected using ML, following which the network resource for accepted requests is optimally allocated using LP. We demonstrate that the proposed method, which adopts a basic multi-layered neural network, can achieve a high request acceptance ratio and adequate network resource allocation within a 10% difference compared to the ideal solution. In addition, the request judgment time of the proposed method is sufficiently short, at less than 1 ms, to achieve an instantaneous response.