Handwritten signatures are a widespread biometric trait for person identification and verification. Reliable authentication and authorization of individuals are, however, challenging tasks due to possible skilled forgeries; especially when a forger has access to a given signature and deliberately tries to imitate it. This problem is even more emphasised in offline signature verification, where dynamic signature information is lost, resulting, as a consequence, in an increased difficulty discerning between genuine and forged signatures. To address this issue, solutions based on convolutional neural networks (CNN) are currently being devised to automatically extract features from a signature. Although highly performing, these methods require a high number of learnable parameters to produce meaningful signature representations, ultimately leading to long training times. In this paper, the R-SigNet architecture, a multi-task approach exploiting a relaxed loss to learn a reduced feature space for writer-independent (WI) signature verification, is presented. Compact generic features are automatically extracted by this network, so that a support vector machine (SVM) can be trained and tested in offline writer-dependent (WD) mode. By leveraging a small generic feature space, the proposed system achieves improved performances and reduced training times with respect to the current literature, as shown by the results obtained on several benchmark datasets.