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

TL;DR

This paper introduces a unified theoretical framework for multi-source transfer learning that jointly optimizes source weights and transfer quantities, supported by an algorithm and validated through experiments.

Contribution

It presents a novel asymptotic framework, UOWQ, that jointly determines optimal source weights and transfer quantities, incorporating Fisher information and parameter discrepancy.

Findings

Using all available source samples is optimal with proper weighting.

The optimal source weights depend on Fisher information and parameter differences.

UOWQ outperforms baseline methods on real-world benchmarks.

Abstract

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.