Functional Stability and Adaptive Control in LLM-Based Computer Use Agents via Graph-Structured Persistent Memory

Large language model (LLM)-driven computer use agents (CUAs) automate graphical user interface (GUI) tasks but often re-solve previously encountered subtasks, increasing token use, latency, and instability. We address this limitation with a directed graph-based persistent memory in which nodes represent observable GUI states and edges encode executable action sequences. We formalize the memory-augmented agent as S=〈A,Σ,G,δ,π,Φ〉, define stability conditions by analogy with functional stability theory, and derive token-cost efficiency bounds. In control-theoretic terms, the Manager–Worker architecture becomes a closed-loop system where memory provides experience-based feedback, and selecting between memory retrieval and fresh LLM planning is treated as adaptive control. Experiments on OSWorld show that the proposed agent cuts both LLM token consumption and execution time by about 50% versus a memoryless baseline while preserving comparable success rates (≈36.9% on 15-step and ≈46.9% on 50-step tasks). Structured graph memory therefore improves robustness under perturbation and supports convergent efficiency gains over time.