# Bootstrapping Post-training Signals for Open-ended Tasks via Rubric-based Self-play on Pre-training Text

arXiv: https://arxiv.org/abs/2604.20051 · HTML: https://mlsanity.com/paper/2604.20051/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Self-play RL for reasoning, one of 13 directions in Synthetic data and self-improvement for LLMs.
- Builds on 43 of its 55 references that are in the map.
- First posted on arXiv 21 Apr 2026.

## Placed in

- Synthetic data and self-improvement for LLMs / [Self-play RL for reasoning](https://mlsanity.com/synth/self-play-rl-for-reasoning/)

## Builds on (most cited first, 30 of 43)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Scaling Instruction-Finetuned Language Models](https://mlsanity.com/paper/2210.11416/) (2022)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [What Disease does this Patient Have? A Large-scale Open Domain Question Answering Dataset from Medical Exams](https://mlsanity.com/paper/2009.13081/) (2020)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [DeepSeek-V3.2: Pushing the Frontier of Open Large Language Models](https://mlsanity.com/paper/2512.02556/) (2025)
- [Self-Rewarding Language Models](https://mlsanity.com/paper/2401.10020/) (2024)
- [Large Language Models Can Self-Improve](https://mlsanity.com/paper/2210.11610/) (2022)
- [MedMCQA : A Large-scale Multi-Subject Multi-Choice Dataset for Medical domain Question Answering](https://mlsanity.com/paper/2203.14371/) (2022)
- [HealthBench: Evaluating Large Language Models Towards Improved Human Health](https://mlsanity.com/paper/2505.08775/) (2025)
- [Rubrics as Rewards: Reinforcement Learning Beyond Verifiable Domains](https://mlsanity.com/paper/2507.17746/) (2025)
- [Absolute Zero: Reinforced Self-play Reasoning with Zero Data](https://mlsanity.com/paper/2505.03335/) (2025)
- [R-Zero: Self-Evolving Reasoning LLM from Zero Data](https://mlsanity.com/paper/2508.05004/) (2025)
- [Will we run out of data? Limits of LLM scaling based on human-generated data](https://mlsanity.com/paper/2211.04325/) (2022)
- [A Minimaximalist Approach to Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2401.04056/) (2024)
- [Checklists Are Better Than Reward Models For Aligning Language Models](https://mlsanity.com/paper/2507.18624/) (2025)
- [DR Tulu: Reinforcement Learning with Evolving Rubrics for Deep Research](https://mlsanity.com/paper/2511.19399/) (2025)
- [Reinforcement Learning with Rubric Anchors](https://mlsanity.com/paper/2508.12790/) (2025)
- [Understanding the performance gap between online and offline alignment algorithms](https://mlsanity.com/paper/2405.08448/) (2024)
- [Agentic Large Language Models, a survey](https://mlsanity.com/paper/2503.23037/) (2025)
- [Learning Dynamics of LLM Finetuning](https://mlsanity.com/paper/2407.10490/) (2024)

## Built on by (most cited first, 5 of 5)

- [From Holistic Evaluation to Structured Criteria: Rubrics Across the Evolving LLM Landscape](https://mlsanity.com/paper/2606.08625/) (2026)
- [SERPO: Self-Evolving Rubric Policy Optimization for Open-Ended Test-Time Reinforcement Learning](https://mlsanity.com/paper/2607.26873/) (2026)
- [A Primer in Post-Training Reasoning Data: What We Know About How It Works](https://mlsanity.com/paper/2606.02113/) (2026)
- [J-Zero: Unified Challenger--Solver--Judge Self-Evolution from Zero Data](https://mlsanity.com/paper/2608.26582/) (2026)
- [From Judgment Quality to Downstream Utility: Rethinking LLM-as-a-Judge for Open-Ended Tasks](https://mlsanity.com/paper/2609.37145/) (2026)

## Abstract (arXiv)

Self-play has recently emerged as a promising paradigm for post-training Large Language Models (LLMs). In self-play, the target LLM creates the task input (e.g., a question), which it then addresses itself by producing a task output (e.g., an answer). A reward model evaluates the output, and the rewards are used to train the LLM, typically via Reinforcement Learning (RL). A key benefit of self-play for post-training LLMs is its minimal supervision costs: self-play avoids the need for high-quality input-output pairs traditionally constructed by humans or expensive proprietary models. Existing work, however, explores self-play only for verifiable tasks, such as math and coding, for which objective ground truth is available and easily checkable. In this paper, we seek to extend self-play to more realistic open-ended tasks. We propose POP, a self-play framework that uses the same LLM to synthesize evaluation rubrics along with each input-output pair. The rubric is used to evaluate outputs and train the model. Crucially, we ground the framework on a content-rich pretraining corpus to (1) enable an exploitable generation-verification gap and reduce reward hacking, and (2) prevent mode collapse. On Qwen-2.5-7B, POP increases performance of both the pretrained base model and instruction-tuned model on multiple tasks ranging from long-form healthcare QA to creative writing and instruction following.