The growing size of large language models (LLMs) requires parameter-efficient fine-tuning (PEFT) methods for their adaptation to new tasks. Existing methods, such as Low-Rank Adaptation (LoRA), typically involve model adaptation by training the PEFT parameters. One open problem required to be solved to effectively employ these methods is the identification of PEFT parameters. More precisely, related works identify PEFT parameters by projecting high dimensional parameters of LLMs onto low dimensional parameter manifolds with predefined projections, or identifying PEFT parameters as projections themselves. To study this problem, we propose a new approach called Learning to Efficiently Fine-tune (LEFT) where we aim to learn spaces of PEFT parameters from data. In order to learn how to generate the PEFT parameters on a learned parameter space while fine-tuning the LLMs, we propose the Parameter Generation (PG) method. In the experimental analyses, we examine the effectiveness of our solutions exploring accuracy of fine-tuned LLMs and characteristics of PEFT parameters on benchmark GLUE tasks.