# Privileged Information Distillation for Language Models

arXiv: https://arxiv.org/abs/2602.04942 · HTML: https://mlsanity.com/paper/2602.04942/

## Key facts

- Cited by 90 papers in the map (data through 14 Oct 2026).
- Placed in On-policy and self-distillation for LLMs, one of 12 directions in Knowledge distillation.
- Builds on 30 of its 41 references that are in the map.
- First posted on arXiv 4 Feb 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 30)

- [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)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [τ-bench: A Benchmark for Tool-Agent-User Interaction in Real-World Domains](https://mlsanity.com/paper/2406.12045/) (2024)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Constructing A Multi-hop QA Dataset for Comprehensive Evaluation of Reasoning Steps](https://mlsanity.com/paper/2011.01060/) (2020)
- [Measuring and Narrowing the Compositionality Gap in Language Models](https://mlsanity.com/paper/2210.03350/) (2022)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [MuSiQue: Multihop Questions via Single-hop Question Composition](https://mlsanity.com/paper/2108.00573/) (2021)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [TravelPlanner: A Benchmark for Real-World Planning with Language Agents](https://mlsanity.com/paper/2402.01622/) (2024)
- [Quiet-STaR: Language Models Can Teach Themselves to Think Before Speaking](https://mlsanity.com/paper/2403.09629/) (2024)
- [Self-Distillation Enables Continual Learning](https://mlsanity.com/paper/2601.19897/) (2026)
- [Learning by Distilling Context](https://mlsanity.com/paper/2209.15189/) (2022)
- [Amortizing intractable inference in large language models](https://mlsanity.com/paper/2310.04363/) (2023)
- [Metacognitive Capabilities of LLMs: An Exploration in Mathematical Problem Solving](https://mlsanity.com/paper/2405.12205/) (2024)
- [START: Self-taught Reasoner with Tools](https://mlsanity.com/paper/2503.04625/) (2025)
- [Joint Prompt Optimization of Stacked LLMs using Variational Inference](https://mlsanity.com/paper/2306.12509/) (2023)
- [Metacognitive Reuse: Turning Recurring LLM Reasoning Into Concise Behaviors](https://mlsanity.com/paper/2509.13237/) (2025)
- [Nudging the Boundaries of LLM Reasoning](https://mlsanity.com/paper/2509.25666/) (2025)
- [Training Plug-n-Play Knowledge Modules with Deep Context Distillation](https://mlsanity.com/paper/2503.08727/) (2025)
- [RLAD: Training LLMs to Discover Abstractions for Solving Reasoning Problems](https://mlsanity.com/paper/2510.02263/) (2025)
- [How to Train Your LLM Web Agent: A Statistical Diagnosis](https://mlsanity.com/paper/2507.04103/) (2025)
- [Language Models Can Learn from Verbal Feedback Without Scalar Rewards](https://mlsanity.com/paper/2509.22638/) (2025)
- [A Comedy of Estimators: On KL Regularization in RL Training of LLMs](https://mlsanity.com/paper/2512.21852/) (2025)
- [Better Estimation of the Kullback--Leibler Divergence Between Language Models](https://mlsanity.com/paper/2504.10637/) (2025)
- [Distilling Rule-based Knowledge into Large Language Models](https://mlsanity.com/paper/2311.08883/) (2023)
- [Variational Reasoning for Language Models](https://mlsanity.com/paper/2509.22637/) (2025)

## Built on by (most cited first, 30 of 90)

- [Learning beyond Teacher: Generalized On-Policy Distillation with Reward Extrapolation](https://mlsanity.com/paper/2602.12125/) (2026)
- [A Survey of On-Policy Distillation for Large Language Models](https://mlsanity.com/paper/2604.00626/) (2026)
- [Self-Distilled RLVR](https://mlsanity.com/paper/2604.03128/) (2026)
- [Why Does Self-Distillation (Sometimes) Degrade the Reasoning Capability of LLMs?](https://mlsanity.com/paper/2603.24472/) (2026)
- [Skill-SD: Skill-Conditioned Self-Distillation for Multi-turn LLM Agents](https://mlsanity.com/paper/2604.10674/) (2026)
- [TCOD: Exploring Temporal Curriculum in On-Policy Distillation for Multi-turn Autonomous Agents](https://mlsanity.com/paper/2604.24005/) (2026)
- [HDPO: Hybrid Distillation Policy Optimization via Privileged Self-Distillation](https://mlsanity.com/paper/2603.23871/) (2026)
- [Embarrassingly Simple Self-Distillation Improves Code Generation](https://mlsanity.com/paper/2604.01193/) (2026)
- [Lightning OPD: Efficient Post-Training for Large Reasoning Models with Offline On-Policy Distillation](https://mlsanity.com/paper/2604.13010/) (2026)
- [Aligning Language Models from User Interactions](https://mlsanity.com/paper/2603.12273/) (2026)
- [Unmasking On-Policy Distillation: Where It Helps, Where It Hurts, and Why](https://mlsanity.com/paper/2605.10889/) (2026)
- [D-OPSD: On-Policy Self-Distillation for Continuously Tuning Step-Distilled Diffusion Models](https://mlsanity.com/paper/2605.05204/) (2026)
- [SOD: Step-wise On-policy Distillation for Small Language Model Agents](https://mlsanity.com/paper/2605.07725/) (2026)
- [Pass the Baton: Trajectory-Relayed On-Policy Distillation](https://mlsanity.com/paper/2607.26057/) (2026)
- [MAD-OPD: Breaking the Ceiling in On-Policy Distillation via Multi-Agent Debate](https://mlsanity.com/paper/2605.01347/) (2026)
- [Are Full Rollouts Necessary for On-Policy Distillation?](https://mlsanity.com/paper/2605.31490/) (2026)
- [On-Policy Self-Distillation without Any Supervision](https://mlsanity.com/paper/2608.06296/) (2026)
- [STEPS: Selective On-Policy Self-Distillation for Reasoning](https://mlsanity.com/paper/2605.10194/) (2026)
- [StepOPSD: Step-Aware Online Preference Self-Distillation for Agent Reinforcement Learning](https://mlsanity.com/paper/2605.27140/) (2026)
- [Trajectory-Refined Distillation](https://mlsanity.com/paper/2606.08432/) (2026)
- [DOPD: Dual On-policy Distillation](https://mlsanity.com/paper/2606.30626/) (2026)
- [Privileged Solutions or Context-Induced Teacher Behavior? Dissecting On-Policy Self-Distillation](https://mlsanity.com/paper/2608.09228/) (2026)
- [HERO: Hindsight-Enhanced Reflection from Environment Observations for Agentic Self-Distillation](https://mlsanity.com/paper/2606.11559/) (2026)
- [Multi-Rollout On-Policy Distillation via Peer Successes and Failures](https://mlsanity.com/paper/2605.12652/) (2026)
- [Tailoring Teaching to Aptitude: Direction-Adaptive Self-Distillation for LLM Reasoning](https://mlsanity.com/paper/2605.22263/) (2026)
- [On-Policy Self-Distillation with Sampled Demonstrations Reduces Output Diversity](https://mlsanity.com/paper/2606.26091/) (2026)
- [From Generic Correlation to Input-Specific Credit in On-Policy Self Distillation](https://mlsanity.com/paper/2605.11613/) (2026)
- [Is More Privileged Information Better? From Solution Traces to Problem-Solving Structure in Self-Distilled Reasoning](https://mlsanity.com/paper/2608.01589/) (2026)
- [Rethinking Privileged Information in On-Policy Self-Distillation](https://mlsanity.com/paper/2608.18271/) (2026)
- [Learning with Rare Success but Rich Feedback via Reflection-Enhanced Self-Distillation](https://mlsanity.com/paper/2605.12741/) (2026)

## Abstract (arXiv)

Training-time privileged information (PI) can enable language models to succeed on tasks they would otherwise fail, making it a powerful tool for reinforcement learning in hard, long-horizon settings. However, transferring capabilities learned with PI to policies that must act without it at inference time remains a fundamental challenge. We study this problem in the context of distilling frontier models for multi-turn agentic environments, which typically hide their internal reasoning and expose only action trajectories. This breaks standard distillation pipelines, since successful behavior is observable, but the reasoning process is not. For this, we introduce π-Distill, a joint teacher-student objective that trains a PI-conditioned teacher and an unconditioned student simultaneously using the same model. Additionally, we also introduce On-Policy Self-Distillation (OPSD), an alternative approach that trains using Reinforcement Learning (RL) with a reverse KL-penalty between the student and the PI-conditioned teacher. We show that both of these algorithms effectively distill frontier agents using action-only PI. Specifically, we find that π-Distill and, in some cases, OPSD, outperform industry standard practices (Supervised finetuning followed by RL) that assume access to full Chain-of-Thought supervision across multiple agentic benchmarks, models, and forms of PI. We complement our results with extensive analysis that characterizes the factors enabling effective learning with PI, focusing primarily on π-Distill and characterizing when OPSD is competitive.