Multi-Task Learning via Generalized Tensor Trace Norm

The trace norm is widely used in multi-task learning as it can discover low-rank structures among tasks in terms of model parameters. Nowadays, with the emerging of big complex datasets and the popularity of deep learning techniques, tensor trace norms have been used for deep multi-task models. However, existing tensor trace norms cannot discover all the low-rank structures and they require users to determine the importance of their components manually. To solve those two issues, in this paper, we propose a Generalized Tensor Trace Norm (GTTN). The GTTN is defined as a convex combination of matrix trace norms of all possible tensor flattenings and hence it can discover all the possible low-rank structures. Based on the induced objective function with the GTTN, we can learn combination coefficients in the GTTN with several strategies. Experiments on real-world datasets demonstrate the effectiveness of the proposed GTTN.