The advent of personalized content generation by LLMs presents a novel challenge: how to efficiently adapt text to meet individual preferences without the unsustainable demand of creating a unique model for each user. This study introduces an innovative online method that employs neural bandit algorithms to dynamically optimize soft instruction embeddings based on user feedback, enhancing the personalization of open-ended text generation by white-box LLMs. Through rigorous experimentation on various tasks, we demonstrate significant performance improvements over baseline strategies. NeuralTS, in particular, leads to substantial enhancements in personalized news headline generation, achieving up to a 62.9% improvement Figure 1: Evolution of generated headlines for an article in terms of best ROUGE scores and on teen internet safety, illustrating the progressive up to 2.76% increase in LLM-agent evaluation refinement of generation that emulates this journalist against the baseline.