# Budget-Aware Agentic Routing via Boundary-Guided Training

arXiv: https://arxiv.org/abs/2602.21227 · HTML: https://mlsanity.com/paper/2602.21227/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in General LLM agent frameworks and benchmarks, one of 16 directions in LLM agents and tool use.
- Builds on 15 of its 21 references that are in the map.
- First posted on arXiv 4 Feb 2026.

## Placed in

- LLM agents and tool use / [General LLM agent frameworks and benchmarks](https://mlsanity.com/agents/general-llm-agent-frameworks-and-benchmarks/)

## Builds on (most cited first, 15 of 15)

- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performance](https://mlsanity.com/paper/2305.05176/) (2023)
- [RouteLLM: Learning to Route LLMs with Preference Data](https://mlsanity.com/paper/2406.18665/) (2024)
- [AppWorld: A Controllable World of Apps and People for Benchmarking Interactive Coding Agents](https://mlsanity.com/paper/2407.18901/) (2024)
- [Hybrid LLM: Cost-Efficient and Quality-Aware Query Routing](https://mlsanity.com/paper/2404.14618/) (2024)
- [ScienceWorld: Is your Agent Smarter than a 5th Grader?](https://mlsanity.com/paper/2203.07540/) (2022)
- [RouterBench: A Benchmark for Multi-LLM Routing System](https://mlsanity.com/paper/2403.12031/) (2024)
- [A Unified Approach to Routing and Cascading for LLMs](https://mlsanity.com/paper/2410.10347/) (2024)
- [Router-R1: Teaching LLMs Multi-Round Routing and Aggregation via Reinforcement Learning](https://mlsanity.com/paper/2506.09033/) (2025)
- [BEST-Route: Adaptive LLM Routing with Test-Time Optimal Compute](https://mlsanity.com/paper/2506.22716/) (2025)
- [RouterEval: A Comprehensive Benchmark for Routing LLMs to Explore Model-level Scaling Up in LLMs](https://mlsanity.com/paper/2503.10657/) (2025)
- [MixLLM: Dynamic Routing in Mixed Large Language Models](https://mlsanity.com/paper/2502.18482/) (2025)
- [CARROT: A Cost Aware Rate Optimal Router](https://mlsanity.com/paper/2502.03261/) (2025)
- [OmniRouter: Budget and Performance Controllable Multi-LLM Routing](https://mlsanity.com/paper/2502.20576/) (2025)
- [Adaptive LLM Routing under Budget Constraints](https://mlsanity.com/paper/2508.21141/) (2025)

## Built on by (most cited first, 10 of 10)

- [AgentCollab: A Self-Evaluation-Driven Collaboration Paradigm for Efficient LLM Agents](https://mlsanity.com/paper/2603.26034/) (2026)
- [Not All Turns Are Equally Hard: Adaptive Thinking Budgets For Efficient Multi-Turn Reasoning in Agents](https://mlsanity.com/paper/2604.05164/) (2026)
- [On Time, Within Budget: Constraint-Driven Online Resource Allocation for Agentic Workflows](https://mlsanity.com/paper/2605.06110/) (2026)
- [SeqRoute: Global Budget-Aware Sequential LLM Routing via Offline Reinforcement Learning](https://mlsanity.com/paper/2605.25424/) (2026)
- [AgentRouter: Heterogeneous Model Routing for Cost-Optimal Multi-Step Agentic Workflows](https://mlsanity.com/paper/2609.22951/) (2026)
- [The Workload-Router-Pool Architecture for LLM Inference Optimization: A Vision Paper from the vLLM Semantic Router Project](https://mlsanity.com/paper/2603.21354/) (2026)
- [RSI-Router: Evolving Subtask-Level LLM Routing and Skills for Cost-Efficient Agents](https://mlsanity.com/paper/2609.34712/) (2026)
- [What Can Component-Replacement Evidence Establish? A Critical Scoping Review of Local Decisions in LLM Agents](https://mlsanity.com/paper/2609.39989/) (2026)
- [Reliability Stress Tests and Decision-Time Routing for Chest X-ray Vision-Language Models](https://mlsanity.com/paper/2610.02270/) (2026)
- [TurnCost: Turns, Not Observations: Cache-Aware Loop Engineering for Coding Agents](https://mlsanity.com/paper/2610.15093/) (2026)

## Abstract (arXiv)

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.