# WDL-OPD: Weak-Driven On-Policy Distillation via Mixture-Constrained Co-Training

arXiv: https://arxiv.org/abs/2608.09447 · HTML: https://mlsanity.com/paper/2608.09447/

## 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 29 of its 34 references that are in the map.
- First posted on arXiv 10 Aug 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, 29 of 29)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Is Your Code Generated by ChatGPT Really Correct? Rigorous Evaluation of Large Language Models for Code Generation](https://mlsanity.com/paper/2305.01210/) (2023)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [BigCodeBench: Benchmarking Code Generation with Diverse Function Calls and Complex Instructions](https://mlsanity.com/paper/2406.15877/) (2024)
- [Policy Distillation](https://mlsanity.com/paper/1511.06295/) (2015)
- [Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe](https://mlsanity.com/paper/2604.13016/) (2026)
- [Latent Collaboration in Multi-Agent Systems](https://mlsanity.com/paper/2511.20639/) (2025)
- [Your Group-Relative Advantage Is Biased](https://mlsanity.com/paper/2601.08521/) (2026)
- [Transformer Copilot: Learning from The Mistake Log in LLM Fine-tuning](https://mlsanity.com/paper/2505.16270/) (2025)
- [Does Your Reasoning Model Implicitly Know When to Stop Thinking?](https://mlsanity.com/paper/2602.08354/) (2026)
- [Learning to Foresee: Unveiling the Unlocking Efficiency of On-Policy Distillation](https://mlsanity.com/paper/2605.11739/) (2026)
- [Heterogeneous Agent Collaborative Reinforcement Learning](https://mlsanity.com/paper/2603.02604/) (2026)
- [On-Policy Delta Distillation](https://mlsanity.com/paper/2607.15161/) (2026)
- [Weak-to-Strong On-Policy Distillation](https://mlsanity.com/paper/2607.26246/) (2026)
- [MASPOB: Bandit-Based Prompt Optimization for Multi-Agent Systems with Graph Neural Networks](https://mlsanity.com/paper/2603.02630/) (2026)
- [Workflow-R1: Group Sub-sequence Policy Optimization for Multi-turn Workflow Construction](https://mlsanity.com/paper/2602.01202/) (2026)
- [SPOT: Sparse Probing and Outcome Calibration for On-Policy Distillation](https://mlsanity.com/paper/2608.04419/) (2026)
- [T-POP: Test-Time Personalization with Online Preference Feedback](https://mlsanity.com/paper/2509.24696/) (2025)
- [Graph-O1 : Monte Carlo Tree Search with Reinforcement Learning for Text-Attributed Graph Reasoning](https://mlsanity.com/paper/2512.17912/) (2025)
- [MIXRAG : Mixture-of-Experts Retrieval-Augmented Generation for Textual Graph Understanding and Question Answering](https://mlsanity.com/paper/2509.21391/) (2025)
- [Weak-Driven Learning: How Weak Agents make Strong Agents Stronger](https://mlsanity.com/paper/2602.08222/) (2026)
- [Simple-OPD: Demystifying Warm-up for On-policy Distillation](https://mlsanity.com/paper/2608.06802/) (2026)
- [Policy Improvement Reinforcement Learning](https://mlsanity.com/paper/2604.00860/) (2026)

## Abstract (arXiv)

On-policy distillation (OPD) aligns a student with a teacher on trajectories sampled from the student itself, reducing the train-test state mismatch of offline distillation. The same feedback loop can nevertheless be unstable: each update changes both the policy and the states on which the next update is computed. We introduce WDL-OPD, a mixture-constrained co-training method with two trainable policies. An anchor policy generates every rollout, an auxiliary policy evaluates the same visited states, and a geometric mixture of their token distributions is matched to a frozen teacher by reverse KL. Both policies receive gradient. We show that freezing the auxiliary recovers an anchor-plus-contrast proxy target closely related to OPD2 and W2S-OPD, whereas joint training creates branch-level degrees of freedom that a static delta cannot express. In recorded Qwen3 experiments at 1.7B and 4B scale, WDL-OPD produces the strongest student checkpoint in each of four scale-domain settings. It raises MATH500 accuracy from 0.630 to 0.685 at 4B and from 0.521 to 0.585 at 1.7B. In code generation, seven single-policy OPD configurations exhibit entropy growth or trajectory degradation, while co-training reaches independently re-evaluated development scores of 0.637 and 0.375. Because several comparisons differ in curriculum or initialization, these results support a stabilization hypothesis rather than a universal causal claim. We provide the exact training algorithm, failure evidence, and the controlled comparison matrix needed to test that hypothesis.