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

TL;DR

A theoretical framework, Unified Optimization of Weights and Quantities (UOWQ), is proposed, which formulates multi-source transfer learning as a parameter estimation problem grounded in an asymptotic analysis of a Kullback-Leibler divergence-based generalization error measure and jointly determines the optimal source weights and optimal transfer quantities for each source task.

Abstract

Transfer learning plays a vital role in improving model performance in data-scarce scenarios. However, naive uniform transfer from multiple source tasks may result in negative transfer, highlighting the need to properly balance the contributions of heterogeneous sources. Moreover, existing transfer learning methods typically focus on optimizing either the source weights or the amount of transferred samples, while largely neglecting the joint consideration of the other. In this work, we propose a theoretical framework, Unified Optimization of Weights and Quantities (UOWQ), which formulates multi-source transfer learning as a parameter estimation problem grounded in an asymptotic analysis of a Kullback-Leibler divergence-based generalization error measure. The proposed framework jointly determines the optimal source weights and optimal transfer quantities for each source task. Firstly, we prove that using all available source samples is always optimal once the weights are properly adjusted, and we provide a theoretical explanation for this phenomenon. Moreover, to determine the optimal transfer weights, our analysis yields closed-form solutions in the single-source setting and develops a convex optimization-based numerical procedure for the multi-source case. Building on the theoretical results, we further propose practical algorithms for both multi-source transfer learning and multi-task learning settings. 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.

Figures (5)

• Figure 1: The three circles represent the errors corresponding to transfer weight $w_1=0$, $w_1^*$, and $w_1>w_1^*$. The distance from each circle’s center to $\theta_0$ represents the bias of estimation, and the radius represents the variance. As the transfer weight of source increases, the bias term increases, while the variance term decreases for $w_1 \in [0,1]$ and increases for $w_1 \in (1, +\infty)$. . The optimal $w_1^*$ achieves the best trade-off between them.
• Figure 2: Overview of the UOWQ training pipeline: At each iteration, the model parameters are optimized via gradient descent using target data together with weighted samples from each source task. The source weights are subsequently updated based on the current model parameters. This alternating optimization procedure establishes an iterative feedback loop that jointly updates the source weights and the target model.
• Figure 3: Overview of the Datasets: Examples from the cross-domain datasets DomainNet and OfficeHome, where images from different domains exhibit distinct visual styles or are captured using different devices.
• Figure 4: Domain preference visualization on DomainNet and Office-Home.
• Figure 5: Performance comparison on the Office-Home dataset under varying target shot settings.

Theorems & Definitions (14)

• Definition 1: The K-L divergence cover1999elements
• Theorem 2
• Proposition 3
• Remark 4: Connection to Prior Work
• Theorem 5
• Remark 6: Explanation of Using All Source Samples
• proof
• Lemma 7
• proof
• Lemma 8