无需调参的多任务学习框架，自动提升高优先级任务性能

Given the ubiquity of multi-task in practical systems, Multi-Task Learning (MTL) has found widespread application across diverse domains. In real-world scenarios, these tasks often have different priorities. For instance, In web search, relevance is often prioritized over other metrics, such as click-through rates or user engagement. Existing frameworks pay insufficient attention to the prioritization among different tasks, which typically adjust task-specific loss function weights to differentiate task priorities. However, this approach encounters challenges as the number of tasks grows, leading to exponential increases in hyper-parameter tuning complexity. Furthermore, the simultaneous optimization of multiple objectives can negatively impact the performance of high-priority tasks due to interference from lower-priority tasks. In this paper, we introduce a novel multi-task learning framework employing Lagrangian Differential Multiplier Methods for step-wise multi-task optimization. It is designed to boost the performance of high-priority tasks without interference from other tasks. Its primary advantage lies in its ability to automatically optimize multiple objectives without requiring balancing hyper-parameters for different tasks, thereby eliminating the need for manual tuning. Additionally, we provide theoretical analysis demonstrating that our method ensures optimization guarantees, enhancing the reliability of the process. We demonstrate its effectiveness through experiments on multiple public datasets and its application in Taobao search, a large-scale industrial search ranking system, resulting in significant improvements across various business metrics.