Sharpness-Aware Cross-Domain Recommendation to Cold-Start Users

TL;DR

This work tackles cold-start cross-domain recommendation by linking transfer learning with loss-geometry through Sharpness-Aware Minimization. It introduces SCDR, a bi-level optimization that pretrains latent factors via Probabilistic Matrix Factorization, learns a sharpness-aware cross-domain mapping $f_U$, and leverages PGD-based perturbations to promote flatter minima in the overlapping-user neighborhood, formalized with $\mathcal{L}_{SCDR}=\max_{\|\boldsymbol{\delta}\|_2\leq \rho}\mathcal{L}_{MF}( (f_U(\hat{\mathbf{u}}^s)+\boldsymbol{\delta};\theta), \hat{\mathbf{v}}^t)$. The theory connects sharpness to generalization bounds and the experiments on Amazon datasets show SCDR consistently outperforms EMCDR baselines, while also improving adversarial robustness. The method proves robust across backbones (MF, NGCF, LightGCN) and provides insights via Lipschitz-based landscape analysis, making it practical for real-world cross-domain cold-start scenarios. Overall, SCDR advances cross-domain transfer by jointly optimizing representation learning and loss geometry, yielding flatter minima and improved generalization under data sparsity.

Abstract

Cross-Domain Recommendation (CDR) is a promising paradigm inspired by transfer learning to solve the cold-start problem in recommender systems. Existing state-of-the-art CDR methods train an explicit mapping function to transfer the cold-start users from a data-rich source domain to a target domain. However, a limitation of these methods is that the mapping function is trained on overlapping users across domains, while only a small number of overlapping users are available for training. By visualizing the loss landscape of the existing CDR model, we find that training on a small number of overlapping users causes the model to converge to sharp minima, leading to poor generalization. Based on this observation, we leverage loss-geometry-based machine learning approach and propose a novel CDR method called Sharpness-Aware CDR (SCDR). Our proposed method simultaneously optimizes recommendation loss and loss sharpness, leading to better generalization with theoretical guarantees. Empirical studies on real-world datasets demonstrate that SCDR significantly outperforms the other CDR models for cold-start recommendation tasks, while concurrently enhancing the model's robustness to adversarial attacks.

Figures (8)

• Figure 1: An example of the EMCDR-based method: it learns an explicit mapping function for users across domains to obtain the representation of cold-start users in the target domain.
• Figure 2: Visualization of loss landscape for user representation space. Compared with the EMCDRman2017cross with a sharp loss landscape, the proposed SCDR converges to a flatter loss landscape on Amazon CDR dataset (Movie $\rightarrow$ Music).
• Figure 3: Illustration of our proposed Sharpness-Aware Cross-Domain Recommendation (SCDR) method. SCDR optimizes the CDR model to converge to a flatter minima through a min-max optimization approach.
• Figure 4: Visualization of loss landscape for representation space around $\hat{\mathbf{u}}^s$. $O$ denotes the ratio of overlapping users.
• Figure 5: Adversarial Robustness of CDR methods.

Theorems & Definitions (1)

• Proposition 1