# Teacher-Guided Tool Learning for Small Language Models via Bidirectional KL Constraints

arXiv: https://arxiv.org/abs/2610.18459 · HTML: https://mlsanity.com/paper/2610.18459/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reinforcement learning for LLM agents, one of 16 directions in LLM agents and tool use.
- Builds on 23 of its 34 references that are in the map.
- First posted on arXiv 13 Oct 2026.

## Placed in

- LLM agents and tool use / [Reinforcement learning for LLM agents](https://mlsanity.com/agents/reinforcement-learning-for-llm-agents/)
- Knowledge distillation / [On-policy and self-distillation for LLMs](https://mlsanity.com/distill/on-policy-and-self-distillation-for-llms/)

## Builds on (most cited first, 23 of 23)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Scheduled Sampling for Sequence Prediction with Recurrent Neural Networks](https://mlsanity.com/paper/1506.03099/) (2015)
- [API-Bank: A Comprehensive Benchmark for Tool-Augmented LLMs](https://mlsanity.com/paper/2304.08244/) (2023)
- [ToolRL: Reward is All Tool Learning Needs](https://mlsanity.com/paper/2504.13958/) (2025)
- [Learning to Reason under Off-Policy Guidance](https://mlsanity.com/paper/2504.14945/) (2025)
- [APIGen: Automated Pipeline for Generating Verifiable and Diverse Function-Calling Datasets](https://mlsanity.com/paper/2406.18518/) (2024)
- [RL's Razor: Why Online Reinforcement Learning Forgets Less](https://mlsanity.com/paper/2509.04259/) (2025)
- [APIGen-MT: Agentic Pipeline for Multi-Turn Data Generation via Simulated Agent-Human Interplay](https://mlsanity.com/paper/2504.03601/) (2025)
- [Learning What Reinforcement Learning Can't: Interleaved Online Fine-Tuning for Hardest Questions](https://mlsanity.com/paper/2506.07527/) (2025)
- [Unifying Group-Relative and Self-Distillation Policy Optimization via Sample Routing](https://mlsanity.com/paper/2604.02288/) (2026)
- [DeepAgent: A General Reasoning Agent with Scalable Toolsets](https://mlsanity.com/paper/2510.21618/) (2025)
- [Distilling LLM Agent into Small Models with Retrieval and Code Tools](https://mlsanity.com/paper/2505.17612/) (2025)
- [KDRL: Post-Training Reasoning LLMs via Unified Knowledge Distillation and Reinforcement Learning](https://mlsanity.com/paper/2506.02208/) (2025)
- [Tool-R0: Self-Evolving LLM Agents for Tool-Learning from Zero Data](https://mlsanity.com/paper/2602.21320/) (2026)
- [TAID: Temporally Adaptive Interpolated Distillation for Efficient Knowledge Transfer in Language Models](https://mlsanity.com/paper/2501.16937/) (2025)
- [LoopTool: Closing the Data-Training Loop for Robust LLM Tool Calls](https://mlsanity.com/paper/2511.09148/) (2025)
- [Distill Where You Fail: Recovering Learning Signals of Negative RL-Groups from Adaptive Teacher Guidance](https://mlsanity.com/paper/2608.00782/) (2026)
- [Teaching LLMs to Learn Tool Trialing and Execution through Environment Interaction](https://mlsanity.com/paper/2601.12762/) (2026)
- [Can Compact Language Models Search Like Agents? Distillation-Guided Policy Optimization for Preserving Agentic RAG Capabilities](https://mlsanity.com/paper/2508.20324/) (2025)
- [STAR: Similarity-guided Teacher-Assisted Refinement for Super-Tiny Function Calling Models](https://mlsanity.com/paper/2602.03022/) (2026)

## Abstract (arXiv)

External tools can extend the capabilities of small language models (SLMs), enabling their deployment in resource constrained environments. However, their limited capabilities make it difficult for SLMs to discover effective tool use behaviors through reinforcement learning alone, while direct teacher supervision suffers from teacher student behavioral distribution mismatch and may propagate erroneous preferences. To address these challenges, we propose Selective Teacher guided Policy Optimization (SeTPO), which coordinates student exploration with selective teacher guidance and persistent demonstration supervision. Specifically, SeTPO incorporates reverse KL derived token level teacher feedback into policy advantages on low reward trajectories, while auxiliary forward KL supervision preserves teacher demonstrated behaviors throughout training. Under an idealized bidirectional KL objective, we theoretically establish that the optimal policy achieves expected reward no lower than the teacher's while retaining a guaranteed fraction of the teacher's probability mass. Extensive experiments on BFCL v4 and API Bank demonstrate that SeTPO achieves superior overall performance over supervised fine tuning, reinforcement learning, and distillation baselines across all three student scales.