# RLVE: Scaling Up Reinforcement Learning for Language Models with Adaptive Verifiable Environments

arXiv: https://arxiv.org/abs/2511.07317 · HTML: https://mlsanity.com/paper/2511.07317/

## Key facts

- Cited by 50 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 61 references that are in the map.
- First posted on arXiv 10 Nov 2025.

## Builds on (most cited first, 30 of 47)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [SGLang: Efficient Execution of Structured Language Model Programs](https://mlsanity.com/paper/2312.07104/) (2023)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Super-NaturalInstructions: Generalization via Declarative Instructions on 1600+ NLP Tasks](https://mlsanity.com/paper/2204.07705/) (2022)
- [Kimi K2: Open Agentic Intelligence](https://mlsanity.com/paper/2507.20534/) (2025)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [Cognitive Behaviors that Enable Self-Improving Reasoners, or, Four Habits of Highly Effective STaRs](https://mlsanity.com/paper/2503.01307/) (2025)
- [Absolute Zero: Reinforced Self-play Reasoning with Zero Data](https://mlsanity.com/paper/2505.03335/) (2025)
- [One Embedder, Any Task: Instruction-Finetuned Text Embeddings](https://mlsanity.com/paper/2212.09741/) (2022)
- [Emergent Tool Use From Multi-Agent Autocurricula](https://mlsanity.com/paper/1909.07528/) (2019)
- [OpenThoughts: Data Recipes for Reasoning Models](https://mlsanity.com/paper/2506.04178/) (2025)
- [DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning](https://mlsanity.com/paper/2504.11456/) (2025)
- [Prioritized Level Replay](https://mlsanity.com/paper/2010.03934/) (2020)
- [Paired Open-Ended Trailblazer (POET): Endlessly Generating Increasingly Complex and Diverse Learning Environments and Their Solutions](https://mlsanity.com/paper/1901.01753/) (2019)
- [Automatic Curriculum Learning For Deep RL: A Short Survey](https://mlsanity.com/paper/2003.04664/) (2020)
- [REASONING GYM: Reasoning Environments for Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2505.24760/) (2025)
- [BIG-Bench Extra Hard](https://mlsanity.com/paper/2502.19187/) (2025)
- [On Memorization of Large Language Models in Logical Reasoning](https://mlsanity.com/paper/2410.23123/) (2024)
- [Self-Evolving Curriculum for LLM Reasoning](https://mlsanity.com/paper/2505.14970/) (2025)

## Built on by (most cited first, 30 of 50)

- [ThetaEvolve: Test-time Learning on Open Problems](https://mlsanity.com/paper/2511.23473/) (2025)
- [From Word to World: Can Large Language Models be Implicit Text-based World Models?](https://mlsanity.com/paper/2512.18832/) (2025)
- [Cognitive Foundations for Reasoning and Their Manifestation in LLMs](https://mlsanity.com/paper/2511.16660/) (2025)
- [RLAnything: Forge Environment, Policy, and Reward Model in Completely Dynamic RL System](https://mlsanity.com/paper/2602.02488/) (2026)
- [Rethinking On-Policy Distillation of Large Language Models II: One Training Example](https://mlsanity.com/paper/2609.04172/) (2026)
- [CUA-Gym: Scaling Verifiable Training Environments and Tasks for Computer-Use Agents](https://mlsanity.com/paper/2605.25624/) (2026)
- [EvoTrainer: Co-Evolving LLM Policies and Training Harnesses for Autonomous Agentic Reinforcement Learning](https://mlsanity.com/paper/2606.03108/) (2026)
- [Environment Scaling for Interactive Agentic Experience Collection: A Survey](https://mlsanity.com/paper/2511.09586/) (2025)
- [SETA: Scaling Environments for Terminal Agents](https://mlsanity.com/paper/2607.10891/) (2026)
- [SPADE: Self-Play in Adaptive Synthetic Executable Environments](https://mlsanity.com/paper/2608.19197/) (2026)
- [Golden Goose: A Simple Trick to Synthesize Unlimited RLVR Tasks from Unverifiable Internet Text](https://mlsanity.com/paper/2601.22975/) (2026)
- [SCALER:Synthetic Scalable Adaptive Learning Environment for Reasoning](https://mlsanity.com/paper/2601.04809/) (2026)
- [Learning to Build the Environment: Self-Evolving Reasoning RL via Verifiable Environment Synthesis](https://mlsanity.com/paper/2605.14392/) (2026)
- [Agentic Environment Engineering for Large Language Models: A Survey of Environment Modeling, Synthesis, Evaluation, and Application](https://mlsanity.com/paper/2606.12191/) (2026)
- [Frontis-MA1: Training an AI4AI Model towards Recursive Self-Improvement in Machine Learning Engineering](https://mlsanity.com/paper/2607.28568/) (2026)
- [Do We Need Adam? Surprisingly Strong and Sparse Reinforcement Learning with SGD in LLMs](https://mlsanity.com/paper/2602.07729/) (2026)
- [Composition-RL: Compose Your Verifiable Prompts for Reinforcement Learning of Large Language Models](https://mlsanity.com/paper/2602.12036/) (2026)
- [IsoCompute Playbook: Optimally Scaling Sampling Compute for LLM RL](https://mlsanity.com/paper/2603.12151/) (2026)
- [LongCoT: Benchmarking Long-Horizon Chain-of-Thought Reasoning](https://mlsanity.com/paper/2604.14140/) (2026)
- [Data Science and Technology Towards AGI Part I: Tiered Data Management](https://mlsanity.com/paper/2602.09003/) (2026)
- [Learning to Reason with Curriculum I: Provable Benefits of Autocurriculum](https://mlsanity.com/paper/2603.18325/) (2026)
- [ZAYA1-8B Technical Report](https://mlsanity.com/paper/2605.05365/) (2026)
- [Training Reasoning Models on Saturated Problems via Failure-Prefix Conditioning](https://mlsanity.com/paper/2601.20829/) (2026)
- [Gym-V: A Unified Vision Environment System for Agentic Vision Research](https://mlsanity.com/paper/2603.15432/) (2026)
- [S3-R1: Learning to Retrieve and Answer Step-by-Step with Synthetic Data](https://mlsanity.com/paper/2605.01248/) (2026)
- [TRON: Targeted Rule-Verifiable Online Environments for Visual Reasoning RL](https://mlsanity.com/paper/2606.01599/) (2026)
- [DocArena: Turning Raw Documents into Controllable Training Environments for Document Search Agents](https://mlsanity.com/paper/2606.26122/) (2026)
- [Learning to Reason with Curriculum II: Compositional Generalization](https://mlsanity.com/paper/2606.27721/) (2026)
- [Beyond Simply Environment Scaling: Designing Effective Environment Distributions for Multimodal Agent Learning](https://mlsanity.com/paper/2608.03571/) (2026)
- [Code2Math: Can Your Code Agent Effectively Evolve Math Problems Through Exploration?](https://mlsanity.com/paper/2603.03202/) (2026)

## Abstract (arXiv)

We introduce Reinforcement Learning (RL) with Adaptive Verifiable Environments (RLVE), an approach using verifiable environments that procedurally generate problems and provide algorithmically verifiable rewards, to scale up RL for language models (LMs). RLVE enables each verifiable environment to dynamically adapt its problem difficulty distribution to the policy model's capabilities as training progresses. In contrast, static data distributions often lead to vanishing learning signals when problems are either too easy or too hard for the policy. To implement RLVE, we create RLVE-Gym, a large-scale suite of 400 verifiable environments carefully developed through manual environment engineering. Using RLVE-Gym, we show that environment scaling, i.e., expanding the collection of training environments, consistently improves generalizable reasoning capabilities. RLVE with joint training across all 400 environments in RLVE-Gym yields a 3.37% absolute average improvement across six reasoning benchmarks, starting from one of the strongest 1.5B reasoning LMs. By comparison, continuing this LM's original RL training yields only a 0.49% average absolute gain despite using over 3x more compute. We release our code publicly.