# AdviSD: Learning to Advise Frontier LLMs via Targeted Multi-Turn Self-Distillation

arXiv: https://arxiv.org/abs/2609.38142 · HTML: https://mlsanity.com/paper/2609.38142/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in On-policy and self-distillation for LLMs, one of 12 directions in Knowledge distillation.
- Builds on 39 of its 47 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Placed in

- 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, 30 of 39)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [ExpeL: LLM Agents Are Experiential Learners](https://mlsanity.com/paper/2308.10144/) (2023)
- [Counterfactual Multi-Agent Policy Gradients](https://mlsanity.com/paper/1705.08926/) (2017)
- [Automatic Prompt Optimization with "Gradient Descent" and Beam Search](https://mlsanity.com/paper/2305.03495/) (2023)
- [τ2-Bench: Evaluating Conversational Agents in a Dual-Control Environment](https://mlsanity.com/paper/2506.07982/) (2025)
- [YaRN: Efficient Context Window Extension of Large Language Models](https://mlsanity.com/paper/2309.00071/) (2023)
- [GEPA: Reflective Prompt Evolution Can Outperform Reinforcement Learning](https://mlsanity.com/paper/2507.19457/) (2025)
- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [From Quantity to Quality: Boosting LLM Performance with Self-Guided Data Selection for Instruction Tuning](https://mlsanity.com/paper/2308.12032/) (2023)
- [Understanding Dataset Difficulty with V-Usable Information](https://mlsanity.com/paper/2110.08420/) (2021)
- [Unifying distillation and privileged information](https://mlsanity.com/paper/1511.03643/) (2015)
- [Self-Distilled RLVR](https://mlsanity.com/paper/2604.03128/) (2026)
- [Guiding Large Language Models via Directional Stimulus Prompting](https://mlsanity.com/paper/2302.11520/) (2023)
- [Tuning Language Models by Proxy](https://mlsanity.com/paper/2401.08565/) (2024)
- [ACEBench: Who Wins the Match Point in Tool Usage?](https://mlsanity.com/paper/2501.12851/) (2025)
- [EnvScaler: Scaling Tool-Interactive Environments for LLM Agent via Programmatic Synthesis](https://mlsanity.com/paper/2601.05808/) (2026)
- [Selective Reflection-Tuning: Student-Selected Data Recycling for LLM Instruction-Tuning](https://mlsanity.com/paper/2402.10110/) (2024)
- [ToolHop: A Query-Driven Benchmark for Evaluating Large Language Models in Multi-Hop Tool Use](https://mlsanity.com/paper/2501.02506/) (2025)
- [Measuring and Increasing Context Usage in Context-Aware Machine Translation](https://mlsanity.com/paper/2105.03482/) (2021)
- [RoTBench: A Multi-Level Benchmark for Evaluating the Robustness of Large Language Models in Tool Learning](https://mlsanity.com/paper/2401.08326/) (2024)
- [RLCSD: Reinforcement Learning with Contrastive On-Policy Self-Distillation](https://mlsanity.com/paper/2606.11709/) (2026)
- [How to Train Your Advisor: Steering Black-Box LLMs with Advisor Models](https://mlsanity.com/paper/2510.02453/) (2025)
- [STEPS: Selective On-Policy Self-Distillation for Reasoning](https://mlsanity.com/paper/2605.10194/) (2026)
- [SAGE-OPD: Selective Agent-Guided Intervention for Multi-Turn On-Policy Distillation](https://mlsanity.com/paper/2606.19659/) (2026)
- [HERO: Hindsight-Enhanced Reflection from Environment Observations for Agentic Self-Distillation](https://mlsanity.com/paper/2606.11559/) (2026)
- [Distill Where You Fail: Recovering Learning Signals of Negative RL-Groups from Adaptive Teacher Guidance](https://mlsanity.com/paper/2608.00782/) (2026)

## Abstract (arXiv)

A small trainable advisor can steer a frozen language-model executor using natural-language advice. In addition to learning from task rewards, the advisor can use feedback from completed interactions to improve its advice. However, a plausible correction need not change execution, yet learning from such corrections can still affect the advisor's future decisions in other contexts. In a shared-parameter model, we prove that such corrections can limit learning if their targets favor useful advice less strongly than those of other corrections. Keeping them less often than the rest improves the model's eventual performance compared to learning from every correction. Motivated by this, our method, Advisor Self-Distillation (AdviSD), pairs outcome-based reinforcement learning with self-distillation from a feedback-conditioned copy of the advisor selectively. Reflection proposes corrections, and the advisor scores the same recorded executor response with and without its issued advice, using the magnitude of the difference to select decisions for supervision. This approach does not require executor likelihoods or additional executor rollouts. Experiments with Qwen3-8B advisors for Gemini and Claude show that AdviSD outperforms advisor-GRPO by 4.2-6.4 percentage points on BFCL-v3 and by 3.9-5.1 score points on EnvScaler. The trained advisors generalize to out-of-domain tasks and transfer across different executor versions and model families. AdviSD also beats matched-count random selection, supporting the value of its selection rule.