The use of large language models (LLMs) is rapidly expanding due to their impressive performance across various tasks . However, as newer versions continue to improve results, their increasing size poses challenges for maintaining multiple domain-specialized versions. The Low-Rank Adaptation (LoRA) method offers a solution to this limitation by enabling fine-tuning modifications to be stored in a file of just a few megabytes, significantly reducing storage requirements. In Machine Translation (MT), models are often specialized for specific domains or language pairs. In our case, we apply these models within Interactive Machine Translation (IMT), where generating high-quality translations and adapting effectively to user modifications are crucial. We have integrated Reinforcement Learning (RL) techniques, optimizing the model using various evaluation metrics. Our results demonstrate that these methods effectively improve translation quality; however, in some cases, this improvement comes at the cost of a slight reduction in generalization capability.