Applying pre-trained language models to new domains through full fine-tuning is computationally expensive and prone to catastrophic forgetting. To address this limitation, we introduce a novel parameter-efficient strategy for unsupervised domain adaptation that combines a custom PEFT architecture with mixed-objective training. The proposed method integrates invertible adapters with Low-Rank Adaptation (LoRA) and jointly optimizes classification on labeled source-domain data and masked language modeling on unlabeled target-domain data. This joint training scheme supports task adaptation while preserving knowledge of the target domain. We evaluate the method on the Multi-Genre Natural Language Inference (MNLI) dataset across 20 domain shifts. Our approach achieves average performance improvements of 1.41 percentage points over the parameter-efficient state-of-the-art UDapter, 1.26 percentage points over the fully tuned DANN baseline, and 0.86 percentage points over DSN, while updating only 7% of the model parameters. These findings establish a new state-of-the-art result for parameter-efficient unsupervised domain adaptation and demonstrate that carefully designed PEFT combinations with concurrent optimization can outperform both parameter-efficient and conventional fully tuned approaches.

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