MOTIVATION: Inferring gene regulatory networks (GRNs) from expression data is a significant systems biology problem. A useful inference algorithm should not only unveil the global structure of the regulatory mechanisms but also the details of regulatory interactions such as edge direction (from regulator to target) and sign (activation/inhibition). Many popular GRN inference algorithms cannot infer edge signs, and those that can infer signed GRNs cannot simultaneously infer edge directions or network cycles. RESULTS: To address these limitations of existing algorithms, we propose Polynomial Lasso Bagging (PoLoBag) for signed GRN inference with both edge directions and network cycles. PoLoBag is an ensemble regression algorithm in a bagging framework where Lasso weights estimated on bootstrap samples are averaged. These bootstrap samples incorporate polynomial features to capture higher-order interactions. Results demonstrate that PoLoBag is consistently more accurate for signed inference than state-of-the-art algorithms on simulated and real-world expression datasets. AVAILABILITY AND IMPLEMENTATION: Algorithm and data are freely available at https://github.com/gourabghoshroy/PoLoBag. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.