MAPRO: Recasting Multi-Agent Prompt Optimization as Maximum a Posteriori Inference

2025-10-08

AI Summary

Multi-agent system (MAS) prompt design suffers from prompt sensitivity, ambiguous credit assignment, and combinatorial explosion of the search space. This paper pioneers a maximum a posteriori (MAP) inference formulation for multi-agent prompt optimization and proposes MAPRO—a four-stage collaborative optimization framework. MAPRO integrates a language-guided max-product belief propagation algorithm, a topology-aware prompt refinement mechanism, and an iterative update strategy driven by execution feedback and downstream attribution. By unifying probabilistic inference with structural and behavioral signals, MAPRO systematically addresses both ambiguous credit assignment and high-dimensional combinatorial search. Evaluated across multiple benchmark tasks, MAPRO significantly outperforms handcrafted prompts and state-of-the-art automated methods, enhancing MAS stability and collaborative efficiency. The framework establishes a novel paradigm for interpretable, scalable, and principled multi-agent prompt optimization.

Technology Category

• Multiagent Systems: Multiagent Planning
• Search and Optimization: Learning to Search
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Search and Retrieval-Augmented AI: Agentic search
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Large language models (LLMs) have demonstrated remarkable capabilities across diverse tasks, and LLM-based agents further extend these abilities to various practical workflows. While recent progress shows that multi-agent systems (MAS) can outperform single agents by coordinating specialized roles, designing effective MAS remains difficult due to prompt sensitivity and the compounded instability MAS creates. To cope with the challenge, recent efforts in automated prompt design have reduced manual effort. However, multi-agent prompt optimization remains largely unexplored. Challenges like exponentially expanding search space and ambiguous credit assignment together make systematic design intractable without principled methods. Therefore, we introduce M}ulti-Agent PRompt Optimization (MAPRO), a four-stage framework that first formulates MAS prompt optimization as a Maximum a Posteriori (MAP) inference problem and solves it using a language-guided variant of max-product belief propagation algorithm. To address credit assignment and updates the system iteratively, MAPRO employs a topology-aware refinement mechanism that integrates execution feedback and downstream blames to selectively update agent prompts. Through this process, MAPRO progressively converges to a coordinated set of agent-specific prompt policies. Across benchmarks in various tasks, MAPRO achieves state-of-the-art performance, consistently surpassing manually engineered baselines and recent automated alternatives. Beyond performance, our MAP-based formulation also delivers general guidelines for building more reliable and principled multi-agent systems in the future

Problem

• Optimizing multi-agent prompts as maximum a posteriori inference problem
• Addressing exponential search space and ambiguous credit assignment challenges
• Developing coordinated agent-specific prompt policies through iterative refinement

Innovation

• Formulates MAS prompt optimization as MAP inference problem
• Solves optimization using language-guided max-product belief propagation
• Employs topology-aware refinement for iterative credit assignment