Bridging Theory and Practice in Source-Free Domain Adaptation via Adversarial Proxy Perturbation

Domain adaptation addresses the distributional shifts be-tween source and target domains. Given increasing data privacy con-straints, Source-Free Domain Adaptation (SFDA) has attracted growinginterest, as it precludes access to raw source data during adaptation.While existing SFDA methods predominantly rely on source-like datageneration or heuristic pseudo-labeling, their connection to target errorgeneralization is often unclear. In this work, we first present a theoreticalanalysis by establishing an upper bound on the target error that over-comes explicit dependence on the classical joint-error term. Guided bythis analysis, we propose an optimization principle based on AdversarialProxy Perturbation (APP), serving as a practical bridge between thederived bound and empirical training. We further extend the frameworkto multi-source scenarios and enable the integration of zero-shot priorsfrom vision-language models (e.g., CLIP) through mutual distillation.Extensive experiments on standard benchmarks demonstrate consistentimprovements over state-of-the-art methods in both unimodal and multi-modal settings, validating the proposed theoretical framework in practice.