Multi-Task Learning (MTL) aims to simultaneously solve a group of related learning tasks by leveraging the salutary knowledge memes contained in the multiple tasks to improve the generalization performance. Many prevalent approaches focus on designing a sophisticated cost function, which integrates all the learning tasks and explores the task-task relationship in a predefined manner. Different from previous approaches, in this paper, we propose a novel Multi-task Gradient Descent (MGD) framework, which improves the generalization performance of multiple tasks through knowledge transfer. The uniqueness of MGD lies in assuming individual task-specific learning objectives at the start, but with the cost functions implicitly changing during the course of parameter optimization based on task-task relationships. Specifically, MGD optimizes the individual cost function of each task using a reformative gradient descent iteration, where relations to other tasks are facilitated through effectively transferring parameter values (serving as the computational representations of memes) from other tasks. Theoretical analysis shows that the proposed framework is convergent under any appropriate transfer mechanism. Compared with existing MTL approaches, MGD provides a novel easy-to-implement framework for MTL, which can mitigate negative transfer in the learning procedure by asymmetric transfer. The proposed MGD has been compared with both classical and state-of-the-art approaches on multiple MTL datasets. The competitive experimental results validate the effectiveness of the proposed algorithm.

多任务学习（MTL）旨在通过利用多个任务中包含的有益知识模因来同时解决一组相关的学习任务，以提高泛化性能。许多流行的方法集中于设计复杂的成本函数，该函数集成了所有学习任务并以预定方式探索任务与任务之间的关系。与以前的方法不同，本文提出了一种新颖的多任务梯度下降（MGD）框架，该框架通过知识转移提高了多任务的泛化性能。MGD的独特之处在于，一开始就假设了各个任务的学习目标，但隐含了成本函数在基于任务-任务关系的参数优化过程中进行更改。具体而言，MGD使用重新构造的梯度下降迭代优化了每个任务的单个成本函数，其中通过有效地传递其他任务的参数值（用作模因的计算表示）来促进与其他任务的关系。理论分析表明，所提出的框架在任何适当的转移机制下都是收敛的。与现有的MTL方法相比，MGD为MTL提供了一种易于实现的新颖框架，该框架可以通过非对称转移减轻学习过程中的负转移。拟议的MGD已在多个MTL数据集上与经典方法和最新方法进行了比较。