# Trust Is Not Enough: Influence Calibration for On-Policy Self-Distillation in Agentic RL

arXiv: https://arxiv.org/abs/2608.14945 · HTML: https://mlsanity.com/paper/2608.14945/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for LLM agents, one of 16 directions in LLM agents and tool use.
- Builds on 24 of its 26 references that are in the map.
- First posted on arXiv 14 Aug 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, 24 of 24)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Search-R1: Training LLMs to Reason and Leverage Search Engines with Reinforcement Learning](https://mlsanity.com/paper/2503.09516/) (2025)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [WebShop: Towards Scalable Real-World Web Interaction with Grounded Language Agents](https://mlsanity.com/paper/2207.01206/) (2022)
- [ALFWorld: Aligning Text and Embodied Environments for Interactive Learning](https://mlsanity.com/paper/2010.03768/) (2020)
- [GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networks](https://mlsanity.com/paper/1711.02257/) (2017)
- [Group-in-Group Policy Optimization for LLM Agent Training](https://mlsanity.com/paper/2505.10978/) (2025)
- [TIP: Token Importance in On-Policy Distillation](https://mlsanity.com/paper/2604.14084/) (2026)
- [Adapting Auxiliary Losses Using Gradient Similarity](https://mlsanity.com/paper/1812.02224/) (2018)
- [Self-Distilled Agentic Reinforcement Learning](https://mlsanity.com/paper/2605.15155/) (2026)
- [RLCSD: Reinforcement Learning with Contrastive On-Policy Self-Distillation](https://mlsanity.com/paper/2606.11709/) (2026)
- [Rethinking On-Policy Self-Distillation for Thinking Models](https://mlsanity.com/paper/2607.05184/) (2026)
- [When Are Teacher Tokens Reliable? Position-Weighted On-Policy Self-Distillation for Reasoning](https://mlsanity.com/paper/2605.21606/) (2026)
- [On the Position Bias of On-Policy Distillation](https://mlsanity.com/paper/2606.22600/) (2026)
- [Respecting Self-Uncertainty in On-Policy Self-Distillation for Efficient LLM Reasoning](https://mlsanity.com/paper/2605.13255/) (2026)
- [SAGE-OPD: Selective Agent-Guided Intervention for Multi-Turn On-Policy Distillation](https://mlsanity.com/paper/2606.19659/) (2026)
- [SG-OPD: Sign-Gated On-Policy Distillation via Sign-Consistency Gating and Phased Teacher Sampling](https://mlsanity.com/paper/2606.09304/) (2026)
- [DOPD: Dual On-policy Distillation](https://mlsanity.com/paper/2606.30626/) (2026)
- [From Generic Correlation to Input-Specific Credit in On-Policy Self Distillation](https://mlsanity.com/paper/2605.11613/) (2026)
- [CRAFT: Counterfactual Credit Assignment from Free Sibling Rollouts for Self-Distilled Agentic Reinforcement Learning](https://mlsanity.com/paper/2606.29476/) (2026)
- [PBSD: Privileged Bayesian Self-Distillation for Long-Horizon Credit Assignment](https://mlsanity.com/paper/2606.09348/) (2026)

## Built on by (most cited first, 3 of 3)

- [AtomRec: Evolving Atomic Memory for Agentic Recommendation](https://mlsanity.com/paper/2609.04882/) (2026)
- [TIDE: Teacher-Student Transition via Informative Distillation and Exploration for Agentic RL](https://mlsanity.com/paper/2609.35058/) (2026)
- [More Methods, Better Agents? A Reality Check on Self-Distillation in Agentic Reinforcement Learning](https://mlsanity.com/paper/2610.19789/) (2026)

## Abstract (arXiv)

On-policy self-distillation (OPSD) gives language agents dense token-level supervision from a privileged self-teacher on the policy's own trajectories. Existing methods allocate this supervision mainly by teacher trust, but trust does not reveal whether emphasizing a token supports the current policy objective. We call this the trust-utility mismatch and introduce Influence Calibration for Self-Distillation (ICSD). For each supervised token, ICSD measures the first-order response of its importance-weighted RL surrogate contribution to a teacher-directed output perturbation. Batch-adaptive calibration converts this non-stationary signal into a bounded allocation weight while preserving the original auxiliary-loss mass within each action turn. These detached weights affect only the distillation loss and require no additional model pass. Across ALFWorld, WebShop, and Search-QA, ICSD improves all matched aggregate metrics over trust-only allocation under Group Relative Policy Optimization (GRPO) and Group-in-Group Policy Optimization (GiGPO), across two model families spanning 1.5B to 7B. At 7B, it reaches 96.1% ALFWorld success and a WebShop score of 93.1. Frozen-batch analyses show that ICSD reduces teacher-supported mass assigned to objective-opposed tokens from 60.1% to 37.8% and raises cosine compatibility with the RL gradient by 0.192. A companion repository is avail- able at https://github.com/lanqz7766/Influence-Calibration-for-On-Policy-Self-Distillation-in-Agentic-RL.