Recurrent Neural Networks (RNNs) have been shown to be valuable for constructing Intrusion Detection Systems (IDSs) for network data. They allow determining if a flow is malicious or not already before it is over, making it possible to take action immediately. However, considering the large number of packets that has to be inspected, for example in cloud/fog and edge computing, the question of computational efficiency arises. We show that by using a novel Reinforcement Learning (RL)-based approach called SparseIDS, we can reduce the number of consumed packets by more than three fourths while keeping classification accuracy high. To minimize the computational expenses of the RL-based sampling we show that a shared neural network can be used for both the classifier and the RL logic. Thus, no additional resources are consumed by the sampling in deployment. Comparing to various other sampling techniques, SparseIDS consistently achieves higher classification accuracy by learning to sample only relevant packets. A major novelty of our RL-based approach is that it can not only skip up to a predefined maximum number of samples like other approaches proposed in the domain of Natural Language Processing but can even skip arbitrarily many packets in one step. This enables saving even more computational resources for long sequences. Inspecting SparseIDS's behavior of choosing packets shows that it adopts different sampling strategies for different attack types and network flows. Finally we build an automatic steering mechanism that can guide SparseIDS in deployment to achieve a desired level of sparsity.