Polymath: A Self-Optimizing Agent with Dynamic Hierarchical Workflow

TL;DR

Polymath is a self-optimizing agent that dynamically refines hierarchical workflows using graph optimization and self-reflection, enabling effective problem-solving without labeled data across diverse tasks.

Contribution

The paper introduces Polymath, a novel self-optimizing agent that automates workflow generation and refinement through a code-based, dynamic hierarchical structure without relying on labeled datasets.

Findings

Achieves 8.1% average improvement over baselines

Effectively solves real-world, dynamic problems

Operates across coding, math, and QA tasks

Abstract

Large language models (LLMs) excel at solving complex tasks by executing agentic workflows composed of detailed instructions and structured operations. Yet, building general-purpose agents by manually embedding foundation models into agentic systems such as Chain-of-Thought, Self-Reflection, and ReACT through text interfaces limits scalability and efficiency. Recently, many researchers have sought to automate the generation and optimization of these workflows through code-based representations. However, existing methods often rely on labeled datasets to train and optimize workflows, making them ineffective and inflexible for solving real-world, dynamic problems where labeled data is unavailable. To address this challenge, we introduce Polymath, a self-optimizing agent with dynamic hierarchical workflow that leverages the flexibility of task flow graphs and the expressiveness of code-represented workflows to solve a wide range of real-world, dynamic problems. The proposed optimization methodology integrates multi-grid-inspired graph optimization with a self-reflection-guided evolutionary algorithm to refine workflows without labeled data. Experimental results on six benchmark datasets across coding, math, and multi-turn QA tasks show that Polymath achieves 8.1% average improvement over state-of-the-art baselines.