Prompt engineering has demonstrated remarkable success in enhancing the performance of large language models (LLMs) across diverse tasks. However, most existing prompt optimization methods only focus on the task-level performance, overlooking the importance of query-preferred prompts, which leads to suboptimal performances. Additionally, these methods rely heavily on frequent interactions with LLMs to obtain feedback for guiding the optimization process, incurring substantial redundant interaction costs. In this paper, we introduce Query-dependent Prompt Optimization (QPO), which leverages multi-loop offline reinforcement learning to iteratively fine-tune a small pretrained language model to generate optimal prompts tailored to the input queries, thus significantly improving the prompting effect on the large target LLM. We derive insights from offline prompting demonstration data, which already exists in large quantities as a by-product of benchmarking diverse prompts on open-sourced tasks, thereby circumventing the expenses of online interactions. Furthermore, we continuously augment the offline dataset with the generated prompts in each loop, as the prompts from the fine-tuned model are supposed to outperform the source prompts in the original dataset. These iterative loops bootstrap the model towards generating optimal prompts. Experiments on various LLM scales and diverse NLP and math tasks demonstrate the efficacy and cost-efficiency of our method in both zero-shot and few-shot scenarios.
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