Budget-Aware Agentic Routing via Boundary-Guided Training

• URL: http://arxiv.org/abs/2602.21227v1
• Date: Wed, 04 Feb 2026 07:39:27 GMT
• Title: Budget-Aware Agentic Routing via Boundary-Guided Training
• Authors: Caiqi Zhang, Menglin Xia, Xuchao Zhang, Daniel Madrigal, Ankur Mallick, Samuel Kessler, Victor Ruehle, Saravan Rajmohan,
• Abstract summary: Budget-Aware Agentic Routing selects between a cheap and an expensive model at each step to optimize the cost-success frontier.<n> Boundary-Guided Training builds a difficulty taxonomy to anchor learning under sparse rewards.<n>Experiment results show that our method improves the efficiency frontier, matching strong routing baselines at substantially lower cost.
• Score: 24.0709108941881
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: As large language models (LLMs) evolve into autonomous agents that execute long-horizon workflows, invoking a high-capability model at every step becomes economically unsustainable. While model routing is effective for single-turn queries, agentic routing is a sequential, path-dependent problem: early mistakes compound, feedback is often at the end of the episode, and deployments often demand strict per-task spending limits. We propose Budget-Aware Agentic Routing, which selects between a cheap and an expensive model at each step to optimize the cost--success frontier and to operate under strict per-task budgets. We propose Boundary-Guided Training, which leverages two boundary policies (always-small vs.\ always-large) to build a difficulty taxonomy and to anchor learning under sparse rewards. Our approach warms start with boundary-guided SFT data synthesis via stratified sampling of cost-efficient trajectories, then applies Boundary-Guided Policy Optimization (BoPO), combining boundary-relative rewards with a reference-guided advantage to avoid degenerate cheap-failure solutions. Experiment results show that our method improves the efficiency frontier, matching strong routing baselines at substantially lower cost while demonstrating generalization to strict inference-time budget constraints. Overall, our work establishes a foundational framework for agentic routing, shifting the paradigm from static model selection to dynamic, budget-aware sequential decision-making.

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