Localized Zeroth-Order Prompt Optimization

Wenyang Hu, Yao Shu, Zongmin Yu, Zhaoxuan Wu, Xiaoqiang Lin, Zhongxiang Dai, See-Kiong Ng, Bryan Kian Hsiang Low

Track: long paper (up to 8 pages)

Keywords: in-context prompting, prompt optimization

TL;DR: To help LLMs better understand in-context exemplars, we propose a principled local optimization method to optimize the prompts for black-box LLMs that outperforms all baseline methods in performance and efficency.

Abstract: The efficacy of large language models (LLMs) in understanding and generating natural language has aroused a wide interest in developing prompt-based methods to harness the power of black-box LLMs, especially through the lens of in-context learning. Existing methods usually prioritize a global optimization for finding the global optimum of prompts, which however will perform poorly in certain tasks. This thus motivates us to re-think the necessity of finding a global optimum in prompt optimization. To answer this, we conduct a thorough empirical study on prompt optimization and draw two major insights. Contrasting with the rarity of global optimum, local optima are usually prevalent and well-performed, which can be more worthwhile for efficient prompt optimization (**Insight I**). The choice of the input domain, covering both the generation and the representation of prompts, affects the identification of well-performing local optima (**Insight II**). Inspired by these insights, we propose a novel algorithm, namely *localized zeroth-order prompt optimization* (ZOPO), which incorporates a Neural Tangent Kernel-based derived Gaussian process into standard zeroth-order optimization for an efficient search of well-performing local optima in prompt optimization. Remarkably, ZOPO outperforms existing baselines in terms of both the optimization performance and the query efficiency, which we demonstrate through extensive experiments.

Submission Number: 13