# CompassPlay: Rewarding the Proposer for Where It Moves the Solver

arXiv: https://arxiv.org/abs/2609.32228 · HTML: https://mlsanity.com/paper/2609.32228/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 38 references that are in the map.
- First posted on arXiv 26 Sep 2026.

## Builds on (most cited first, 30 of 34)

- [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)
- [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)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Qwen2.5-Coder Technical Report](https://mlsanity.com/paper/2409.12186/) (2024)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Estimating Training Data Influence by Tracing Gradient Descent](https://mlsanity.com/paper/2002.08484/) (2020)
- [LESS: Selecting Influential Data for Targeted Instruction Tuning](https://mlsanity.com/paper/2402.04333/) (2024)
- [Absolute Zero: Reinforced Self-play Reasoning with Zero Data](https://mlsanity.com/paper/2505.03335/) (2025)
- [CRUXEval: A Benchmark for Code Reasoning, Understanding and Execution](https://mlsanity.com/paper/2401.03065/) (2024)
- [DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition](https://mlsanity.com/paper/2504.21801/) (2025)
- [Emergent Complexity and Zero-shot Transfer via Unsupervised Environment Design](https://mlsanity.com/paper/2012.02096/) (2020)
- [Automatic Goal Generation for Reinforcement Learning Agents](https://mlsanity.com/paper/1705.06366/) (2017)
- [REINFORCE++: Stabilizing Critic-Free Policy Optimization with Global Advantage Normalization](https://mlsanity.com/paper/2501.03262/) (2025)
- [R-Zero: Self-Evolving Reasoning LLM from Zero Data](https://mlsanity.com/paper/2508.05004/) (2025)
- [Teacher-Student Curriculum Learning](https://mlsanity.com/paper/1707.00183/) (2017)
- [Evolving Curricula with Regret-Based Environment Design](https://mlsanity.com/paper/2203.01302/) (2022)
- [Self-Evolving Curriculum for LLM Reasoning](https://mlsanity.com/paper/2505.14970/) (2025)
- [MATES: Model-Aware Data Selection for Efficient Pretraining with Data Influence Models](https://mlsanity.com/paper/2406.06046/) (2024)
- [SPICE: Self-Play In Corpus Environments Improves Reasoning](https://mlsanity.com/paper/2510.24684/) (2025)
- [STP: Self-play LLM Theorem Provers with Iterative Conjecturing and Proving](https://mlsanity.com/paper/2502.00212/) (2025)
- [Learning Formal Mathematics From Intrinsic Motivation](https://mlsanity.com/paper/2407.00695/) (2024)
- [Language Self-Play For Data-Free Training](https://mlsanity.com/paper/2509.07414/) (2025)
- [Montessori-Instruct: Generate Influential Training Data Tailored for Student Learning](https://mlsanity.com/paper/2410.14208/) (2024)
- [Teaching Models to Teach Themselves: Reasoning at the Edge of Learnability](https://mlsanity.com/paper/2601.18778/) (2026)
- [GradAlign: Gradient-Aligned Data Selection for LLM Reinforcement Learning](https://mlsanity.com/paper/2602.21492/) (2026)
- [Scaling Self-Play with Self-Guidance](https://mlsanity.com/paper/2604.20209/) (2026)
- [LearnAlign: Data Selection for LLM Reinforcement Learning with Improved Gradient Alignment](https://mlsanity.com/paper/2506.11480/) (2025)

## Abstract (arXiv)

In self-play, a proposer generates verifiable tasks to train a solver. Proposer rewards often depend on the solver's success rate, but equally difficult tasks can differ in their training value. We introduce CompassPlay, a self-play method that rewards the proposer through gradient alignment. The reward favors tasks whose solver loss gradients align with those of reference tasks representing the target capabilities. It draws on a first-order approximation to learning progress and scores each eligible task without additional solver training. Our experiments show gains in performance and training efficiency. In coding self-play with Qwen2.5-Coder-7B, a small external reference set guides task generation. CompassPlay improves average accuracy over AZR's difficulty reward by 1.5 percentage points on in-domain coding and 2.7 on out-of-domain mathematics. In Lean4 theorem proving, CompassPlay matches the difficulty baseline's 150-iteration cumulative coverage with 40% fewer GPU-hours.