A Survey of Automatic Prompt Engineering: An Optimization Perspective

TL;DR

This survey comprehensively reviews automated prompt engineering methods across modalities, formalizing them as optimization problems and highlighting future research directions in a unified framework.

Contribution

It provides the first unified, optimization-theoretic survey of automated prompt engineering across text, vision, and multimodal models, bridging theory and practice.

Findings

Formalization of prompt optimization as a maximization problem

Systematic organization of methods by variables and objectives

Identification of underexplored areas like constrained optimization

Abstract

The rise of foundation models has shifted focus from resource-intensive fine-tuning to prompt engineering, a paradigm that steers model behavior through input design rather than weight updates. While manual prompt engineering faces limitations in scalability, adaptability, and cross-modal alignment, automated methods, spanning foundation model (FM) based optimization, evolutionary methods, gradient-based optimization, and reinforcement learning, offer promising solutions. Existing surveys, however, remain fragmented across modalities and methodologies. This paper presents the first comprehensive survey on automated prompt engineering through a unified optimization-theoretic lens. We formalize prompt optimization as a maximization problem over discrete, continuous, and hybrid prompt spaces, systematically organizing methods by their optimization variables (instructions, soft prompts, exemplars), task-specific objectives, and computational frameworks. By bridging theoretical formulation with practical implementations across text, vision, and multimodal domains, this survey establishes a foundational framework for both researchers and practitioners, while highlighting underexplored frontiers in constrained optimization and agent-oriented prompt design.