Localized Zeroth-Order Prompt Optimization

TL;DR

This paper challenges the focus on global optimization in prompt tuning for large language models, proposing a localized zeroth-order method that efficiently finds well-performing local optima, improving performance and query efficiency.

Contribution

It introduces ZOPO, a novel localized optimization algorithm using Neural Tangent Kernel-based Gaussian processes for prompt tuning, with demonstrated superior performance.

Findings

ZOPO outperforms existing methods in optimization performance.

ZOPO achieves higher query efficiency in prompt optimization.

Local optima are often more effective than global optima in prompt tuning.

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. Existing methodologies usually prioritize a global optimization for finding the global optimum, 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.