From Agent Loops to Structured Graphs:A Scheduler-Theoretic Framework for LLM Agent Execution

TL;DR

This paper introduces a scheduler-theoretic framework for LLM agents, replacing implicit agent loops with explicit, verifiable graph-based execution plans to improve controllability and debugging.

Contribution

It proposes SGH, a static DAG control flow model for LLM agents, and applies classical scheduling theory to analyze and formalize agent execution.

Findings

Identifies structural weaknesses in the agent loop paradigm.

Provides a formal specification with termination and soundness guarantees.

Offers a survey and analysis of 70 systems for trade-offs in control and expressiveness.

Abstract

The dominant paradigm for building LLM based agents is the Agent Loop, an iterative cycle where a single language model decides what to do next by reading an ever growing context window. This paradigm has three structural weaknesses: implicit dependencies between steps, unbounded recovery loops, and mutable execution history that complicates debugging. We characterize the Agent Loop as a single ready unit scheduler: at any moment, at most one executable unit is active, and the choice of which unit to activate comes from opaque LLM inference rather than an inspectable policy. This perspective places Agent Loops and graph based execution engines on a single semantic continuum. We propose SGH, Structured Graph Harness, which lifts control flow from implicit context into an explicit static DAG. SGH makes three commitments: execution plans are immutable within a plan version, planning execution and recovery are separated into three layers, and recovery follows a strict escalation protocol. These choices trade some expressiveness for controllability, verifiability, and implementability. Our contributions are fourfold: a scheduler unified framework that applies classical scheduling theory to LLM agent execution and identifies challenges introduced by non deterministic LLM nodes; a trade off analysis of controllability, expressiveness, and implementability across 70 surveyed systems; a formal specification including a node state machine with termination and soundness guarantees; and an attributable experimental framework with a seven group design for future validation. This is a position paper and design proposal. We provide a theoretical framework, design analysis, and experimental protocol, not a production implementation or empirical results.