Unified Optimization of Source Weights and Transfer Quantities in Multi-Source Transfer Learning: An Asymptotic Framework

In multi-source transfer learning, a key challenge lies in how to appropriately differentiate and utilize heterogeneous source tasks. However, existing multi-source methods typically focus on optimizing either the source weights or the amount of transferred samples, largely neglecting their joint consideration. In this work, we propose a theoretical framework, Unified Optimization of Weights and Quantities (UOWQ), that jointly determines the optimal source weights and transfer quantities for each source task. Specifically, the framework formulates multi-source transfer learning as a parameter estimation problem based on an asymptotic analysis of a Kullback--Leibler divergence--based generalization error measure, leading to two main theoretical findings: 1) using all available source samples is always optimal when the weights are properly adjusted; 2) the optimal source weights are characterized by a principled optimization problem whose structure explicitly incorporates the Fisher information, parameter discrepancy, parameter dimensionality, and transfer quantities. Building on the theoretical results, we further propose a practical algorithm for multi-source transfer learning, and extend it to multi-task learning settings where each task simultaneously serves as both a source and a target. Extensive experiments on real-world benchmarks, including DomainNet and Office-Home, demonstrate that UOWQ consistently outperforms strong baselines. The results validate both the theoretical predictions and the practical effectiveness of our framework.