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Introducing the BudgetMem framework to address the conflict between performance and cost that occurs during the on-demand memory extraction process of the Large Language Model (LLM) agent. Unlike traditional fixed memory processing, this system introduces a module-specific budget-tier interface to flexibly adjust calculation resources at runtime. Lightweight routers, a key component, determine the optimal cost-effective reasoning path according to the complexity of each query through reinforcement learning. The researchers systematically compared and analyzed the budget control strategy in three aspects: implementation method, reasoning behavior, and model capacity. As a result of the experiment, BudgetMem established an efficient performance boundary with an excellent correct answer rate compared to existing benchmarks even within a limited budget. As a result, this framework enables cost-effective and precise customized memory control, increasing utilization in real-world industrial environments. https://arxiv.org/pdf/2602.06025