Multi--task learning seeks to improve the generalization error by leveraging the common information shared by multiple related tasks. One challenge in multi--task learning is identifying formulations capable of uncovering the common information shared between different but related tasks. This paper provides a precise asymptotic analysis of a popular multi--task formulation associated with misspecified perceptron learning models. The main contribution of this paper is to precisely determine the reasons behind the benefits gained from combining multiple related tasks. Specifically, we show that combining multiple tasks is asymptotically equivalent to a traditional formulation with additional regularization terms that help improve the generalization performance. Another contribution is to empirically study the impact of combining tasks on the generalization error. In particular, we empirically show that the combination of multiple tasks postpones the double descent phenomenon and can mitigate it asymptotically.

翻译：多任务学习旨在通过利用多个相关任务共享的公共信息来改善泛化误差。多任务学习中的一个挑战在于识别能够揭示不同但相关任务之间共享公共信息的公式化方法。本文对一种与误设感知器学习模型相关的流行多任务公式进行了精确的渐近分析。本文的主要贡献在于精确确定了组合多个相关任务带来收益的根本原因。具体而言，我们证明组合多个任务在渐近意义上等价于具有额外正则化项的传统公式化方法，这些正则化项有助于提升泛化性能。另一项贡献是对组合任务如何影响泛化误差进行了实证研究。特别地，我们通过实验证明多任务组合会推迟双下降现象的发生，并能在渐近意义上缓解该现象。