  Automatic prompt optimization is an important approach to improving the
performance of large language models (LLMs). Recent research demonstrates the
potential of using LLMs as prompt optimizers, which can generate improved task
prompts via iterative refinement. In this paper, we propose a novel perspective
to investigate the design of LLM-based prompt optimizers, by drawing an analogy
with gradient-based model optimizers. To connect these two approaches, we
identify two pivotal factors in model parameter learning: update direction and
update method. Focused on the two aspects, we borrow the theoretical framework
and learning methods from gradient-based optimization to design improved
strategies for LLM-based prompt optimizers. By systematically analyzing a rich
set of improvement strategies, we further develop a capable Gradient-inspired
LLM-based Prompt Optimizer called GPO. At each step, it first retrieves
relevant prompts from the optimization trajectory as the update direction.
Then, it utilizes the generation-based refinement strategy to perform the
update, while controlling the edit distance through a cosine-based decay
strategy. Extensive experiments demonstrate the effectiveness and efficiency of
GPO. In particular, GPO brings an additional improvement of up to 56.8% on
Big-Bench Hard and 55.3% on MMLU compared to baseline methods.
