MAPGD: Multi-Agent Prompt Gradient Descent for Collaborative Prompt Optimization

Prompt engineering is crucial for fully leveraging large language models (LLMs), yet most existing optimization methods follow a single trajectory, resulting in limited adaptability, gradient conflicts, and high computational overhead. We propose MAPGD (Multi-Agent Prompt Gradient Descent), a novel framework that reconceptualizes prompt optimization as a collaborative process among specialized agents. Each agent focuses on a distinct refinement dimension, such as instruction clarity, example selection, format structure, or stylistic adaptation, and their contributions are coordinated through semantic gradient embedding, conflict detection, and fusion. To further enhance robustness and stability, MAPGD introduces two new mechanisms: Hypersphere Constrained Gradient Clustering (HCGC), which enforces angular margin constraints for compact and well-separated clusters, and Channel Adaptive Agent Weighting (CAAW), which dynamically reweights agent contributions based on validation performance. Experiments on classification and reasoning benchmarks show that MAPGD consistently surpasses single-agent and random baselines in both accuracy and efficiency. Ablation studies confirm the effectiveness of gradient fusion, agent specialization, and conflict resolution. Together, these components establish MAPGD as a unified, gradient-based, and interpretable framework for robust prompt optimization with theoretical convergence guarantees.