# Self-Evolving Curriculum for LLM Reasoning

arXiv: https://arxiv.org/abs/2505.14970 · HTML: https://mlsanity.com/paper/2505.14970/

## Key facts

- Cited by 112 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 49 of its 69 references that are in the map.
- First posted on arXiv 20 May 2025.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)
- Synthetic data and self-improvement for LLMs / [Synthetic reasoning data and bootstrapping](https://mlsanity.com/synth/synthetic-reasoning-data-and-bootstrapping/)

## Builds on (most cited first, 30 of 49)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [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)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [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)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Prioritized Experience Replay](https://mlsanity.com/paper/1511.05952/) (2015)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [SimPO: Simple Preference Optimization with a Reference-Free Reward](https://mlsanity.com/paper/2405.14734/) (2024)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Training Language Models to Self-Correct via Reinforcement Learning](https://mlsanity.com/paper/2409.12917/) (2024)
- [Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation](https://mlsanity.com/paper/2106.04399/) (2021)
- [Cognitive Behaviors that Enable Self-Improving Reasoners, or, Four Habits of Highly Effective STaRs](https://mlsanity.com/paper/2503.01307/) (2025)
- [Not All Samples Are Created Equal: Deep Learning with Importance Sampling](https://mlsanity.com/paper/1803.00942/) (2018)
- [Demystifying Long Chain-of-Thought Reasoning in LLMs](https://mlsanity.com/paper/2502.03373/) (2025)
- [Emergent Complexity and Zero-shot Transfer via Unsupervised Environment Design](https://mlsanity.com/paper/2012.02096/) (2020)
- [SWE-RL: Advancing LLM Reasoning via Reinforcement Learning on Open Software Evolution](https://mlsanity.com/paper/2502.18449/) (2025)
- [Automatic Goal Generation for Reinforcement Learning Agents](https://mlsanity.com/paper/1705.06366/) (2017)
- [WebRL: Training LLM Web Agents via Self-Evolving Online Curriculum Reinforcement Learning](https://mlsanity.com/paper/2411.02337/) (2024)
- [Teacher-Student Curriculum Learning](https://mlsanity.com/paper/1707.00183/) (2017)

## Built on by (most cited first, 30 of 112)

- [The Landscape of Agentic Reinforcement Learning for LLMs: A Survey](https://mlsanity.com/paper/2509.02547/) (2025)
- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [AutoSkill: Experience-Driven Lifelong Learning via Skill Self-Evolution](https://mlsanity.com/paper/2603.01145/) (2026)
- [Curriculum Reinforcement Learning from Easy to Hard Tasks Improves LLM Reasoning](https://mlsanity.com/paper/2506.06632/) (2025)
- [Can Prompt Difficulty be Online Predicted for Accelerating RL Finetuning of Reasoning Models?](https://mlsanity.com/paper/2507.04632/) (2025)
- [RLVE: Scaling Up Reinforcement Learning for Language Models with Adaptive Verifiable Environments](https://mlsanity.com/paper/2511.07317/) (2025)
- [Maximum Likelihood Reinforcement Learning](https://mlsanity.com/paper/2602.02710/) (2026)
- [Diversity-Incentivized Exploration for Versatile Reasoning](https://mlsanity.com/paper/2509.26209/) (2025)
- [Knapsack RL: Unlocking Exploration of LLMs via Optimizing Budget Allocation](https://mlsanity.com/paper/2509.25849/) (2025)
- [Imbalanced Gradients in RL Post-Training of Multi-Task LLMs](https://mlsanity.com/paper/2510.19178/) (2025)
- [CurES: From Gradient Analysis to Efficient Curriculum Learning for Reasoning LLMs](https://mlsanity.com/paper/2510.01037/) (2025)
- [Can One Domain Help Others? A Data-Centric Study on Multi-Domain Reasoning via Reinforcement Learning](https://mlsanity.com/paper/2507.17512/) (2025)
- [RL for Reasoning by Adaptively Revealing Rationales](https://mlsanity.com/paper/2506.18110/) (2025)
- [BOTS: A Unified Framework for Bayesian Online Task Selection in LLM Reinforcement Finetuning](https://mlsanity.com/paper/2510.26374/) (2025)
- [Graph is a Substrate Across Data Modalities](https://mlsanity.com/paper/2601.22384/) (2026)
- [Small Generalizable Prompt Predictive Models Can Steer Efficient RL Post-Training of Large Reasoning Models](https://mlsanity.com/paper/2602.01970/) (2026)
- [Multi-Task GRPO: Reliable LLM Reasoning Across Tasks](https://mlsanity.com/paper/2602.05547/) (2026)
- [Teaching Models to Teach Themselves: Reasoning at the Edge of Learnability](https://mlsanity.com/paper/2601.18778/) (2026)
- [CoBA-RL: Capability-Oriented Budget Allocation for Reinforcement Learning in LLMs](https://mlsanity.com/paper/2602.03048/) (2026)
- [SPADE: Self-Play in Adaptive Synthetic Executable Environments](https://mlsanity.com/paper/2608.19197/) (2026)
- [What Makes a Good Curriculum? Disentangling the Effects of Data Ordering on LLM Mathematical Reasoning](https://mlsanity.com/paper/2510.19099/) (2025)
- [VADE: Variance-Aware Dynamic Sampling via Online Sample-Level Difficulty Estimation for Multimodal RL](https://mlsanity.com/paper/2511.18902/) (2025)
- [Dynamics-Predictive Sampling for Active RL Finetuning of Large Reasoning Models](https://mlsanity.com/paper/2603.10887/) (2026)
- [CEC-Zero: Zero-Supervision Character Error Correction with Self-Generated Rewards](https://mlsanity.com/paper/2512.23971/) (2025)
- [Train at Moving Edge: Online-Verified Prompt Selection for Efficient RL Training of Large Reasoning Model](https://mlsanity.com/paper/2603.25184/) (2026)
- [TRACE: A Unified Rollout Budget Allocation Framework for Efficient Agentic Reinforcement Learning](https://mlsanity.com/paper/2606.11119/) (2026)
- [Understanding Diversity Collapse in RLVR via the Lens of Overtraining](https://mlsanity.com/paper/2606.15455/) (2026)
- [DynamixSFT: Dynamic Mixture Optimization of Instruction Tuning Collections](https://mlsanity.com/paper/2508.12116/) (2025)
- [LatentEvolve: Self-Evolving Test-Time Scaling in Latent Space](https://mlsanity.com/paper/2509.24771/) (2025)
- [Generate, Filter, Control, Replay: A Comprehensive Survey of Rollout Strategies for LLM Reinforcement Learning](https://mlsanity.com/paper/2605.02913/) (2026)

## Abstract (arXiv)

Reinforcement learning (RL) has proven effective for fine-tuning large language models (LLMs), significantly enhancing their reasoning abilities in domains such as mathematics and code generation. A crucial factor influencing RL fine-tuning success is the training curriculum: the order in which training problems are presented. While random curricula serve as common baselines, they remain suboptimal; manually designed curricula often rely heavily on heuristics, and online filtering methods can be computationally prohibitive. To address these limitations, we propose Self-Evolving Curriculum (SEC), an automatic curriculum learning method that learns a curriculum policy concurrently with the RL fine-tuning process. Our approach formulates curriculum selection as a non-stationary Multi-Armed Bandit problem, treating each problem category (e.g., difficulty level or problem type) as an individual arm. We leverage the absolute advantage from policy gradient methods as a proxy measure for immediate learning gain. At each training step, the curriculum policy selects categories to maximize this reward signal and is updated using the TD(0) method. Across three distinct reasoning domains: planning, inductive reasoning, and mathematics, our experiments demonstrate that SEC significantly improves models' reasoning capabilities, enabling better generalization to harder, out-of-distribution test problems. Additionally, our approach achieves better skill balance when fine-tuning simultaneously on multiple reasoning domains. These findings highlight SEC as a promising strategy for RL fine-tuning of LLMs.