# Tapered Off-Policy REINFORCE: Stable and efficient reinforcement learning for LLMs

arXiv: https://arxiv.org/abs/2503.14286 · HTML: https://mlsanity.com/paper/2503.14286/

## Key facts

- Cited by 61 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 59 references that are in the map.
- First posted on arXiv 18 Mar 2025.

## Builds on (most cited first, 30 of 45)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [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)
- [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)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [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)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems](https://mlsanity.com/paper/2005.01643/) (2020)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [A General Theoretical Paradigm to Understand Learning from Human Preferences](https://mlsanity.com/paper/2310.12036/) (2023)
- [Adafactor: Adaptive Learning Rates with Sublinear Memory Cost](https://mlsanity.com/paper/1804.04235/) (2018)
- [IMPALA: Scalable Distributed Deep-RL with Importance Weighted Actor-Learner Architectures](https://mlsanity.com/paper/1802.01561/) (2018)
- [QT-Opt: Scalable Deep Reinforcement Learning for Vision-Based Robotic Manipulation](https://mlsanity.com/paper/1806.10293/) (2018)
- [Negative Preference Optimization: From Catastrophic Collapse to Effective Unlearning](https://mlsanity.com/paper/2404.05868/) (2024)
- [Reinforced Self-Training (ReST) for Language Modeling](https://mlsanity.com/paper/2308.08998/) (2023)
- [Generative Verifiers: Reward Modeling as Next-Token Prediction](https://mlsanity.com/paper/2408.15240/) (2024)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [Beyond Human Data: Scaling Self-Training for Problem-Solving with Language Models](https://mlsanity.com/paper/2312.06585/) (2023)
- [Safe and Efficient Off-Policy Reinforcement Learning](https://mlsanity.com/paper/1606.02647/) (2016)
- [Direct Language Model Alignment from Online AI Feedback](https://mlsanity.com/paper/2402.04792/) (2024)
- [Preference Fine-Tuning of LLMs Should Leverage Suboptimal, On-Policy Data](https://mlsanity.com/paper/2404.14367/) (2024)
- [Variance-based regularization with convex objectives](https://mlsanity.com/paper/1610.02581/) (2016)
- [Generative Reward Models](https://mlsanity.com/paper/2410.12832/) (2024)

## Built on by (most cited first, 30 of 61)

- [AReaL: A Large-Scale Asynchronous Reinforcement Learning System for Language Reasoning](https://mlsanity.com/paper/2505.24298/) (2025)
- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [A Sober Look at Progress in Language Model Reasoning: Pitfalls and Paths to Reproducibility](https://mlsanity.com/paper/2504.07086/) (2025)
- [On-Policy RL Meets Off-Policy Experts: Harmonizing Supervised Fine-Tuning and Reinforcement Learning via Dynamic Weighting](https://mlsanity.com/paper/2508.11408/) (2025)
- [R1-Reward: Training Multimodal Reward Model Through Stable Reinforcement Learning](https://mlsanity.com/paper/2505.02835/) (2025)
- [Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2504.12501/) (2025)
- [Prosperity before Collapse: How Far Can Off-Policy RL Reach with Stale Data on LLMs?](https://mlsanity.com/paper/2510.01161/) (2025)
- [ExGRPO: Learning to Reason from Experience](https://mlsanity.com/paper/2510.02245/) (2025)
- [BAPO: Stabilizing Off-Policy Reinforcement Learning for LLMs via Balanced Policy Optimization with Adaptive Clipping](https://mlsanity.com/paper/2510.18927/) (2025)
- [PipelineRL: Faster On-policy Reinforcement Learning for Long Sequence Generation](https://mlsanity.com/paper/2509.19128/) (2025)
- [Let It Flow: Agentic Crafting on Rock and Roll, Building the ROME Model within an Open Agentic Learning Ecosystem](https://mlsanity.com/paper/2512.24873/) (2025)
- [Asymmetric REINFORCE for off-Policy Reinforcement Learning: Balancing positive and negative rewards](https://mlsanity.com/paper/2506.20520/) (2025)
- [GRPO-λ: Credit Assignment improves LLM Reasoning](https://mlsanity.com/paper/2510.00194/) (2025)
- [How to Train Your LLM Web Agent: A Statistical Diagnosis](https://mlsanity.com/paper/2507.04103/) (2025)
- [Adaptive Guidance Accelerates Reinforcement Learning of Reasoning Models](https://mlsanity.com/paper/2506.13923/) (2025)
- [Part II: ROLL Flash -- Accelerating RLVR and Agentic Training with Asynchrony](https://mlsanity.com/paper/2510.11345/) (2025)
- [Squeeze the Soaked Sponge: Efficient Off-policy Reinforcement Finetuning for Large Language Model](https://mlsanity.com/paper/2507.06892/) (2025)
- [Don't Waste Mistakes: Leveraging Negative RL-Groups via Confidence Reweighting](https://mlsanity.com/paper/2510.08696/) (2025)
- [VESPO: Variational Sequence-Level Soft Policy Optimization for Stable Off-Policy LLM Training](https://mlsanity.com/paper/2602.10693/) (2026)
- [LLMs Can Learn to Reason Via Off-Policy RL](https://mlsanity.com/paper/2602.19362/) (2026)
- [Stabilizing Off-Policy Training for Long-Horizon LLM Agent via Turn-Level Importance Sampling and Clipping-Triggered Normalization](https://mlsanity.com/paper/2511.20718/) (2025)
- [Rethinking Muon Beyond Pretraining: Spectral Failures and High-Pass Remedies for VLA and RLVR](https://mlsanity.com/paper/2605.19282/) (2026)
- [It's Not You, It's Clipping: A Soft Trust-Region via Probability Smoothing for LLM RL](https://mlsanity.com/paper/2509.21282/) (2025)
- [Polychromic Objectives for Reinforcement Learning](https://mlsanity.com/paper/2509.25424/) (2025)
- [The Era of Agentic Organization: Learning to Organize with Language Models](https://mlsanity.com/paper/2510.26658/) (2025)
- [A Step Back: Prefix Importance Ratio Stabilizes Policy Optimization](https://mlsanity.com/paper/2601.22718/) (2026)
- [How Off-Policy Can GRPO Be? Mu-GRPO for Efficient LLM Reinforcement Learning](https://mlsanity.com/paper/2605.17570/) (2026)
- [Unearthing Gems from Stones: Policy Optimization with Negative Sample Augmentation for LLM Reasoning](https://mlsanity.com/paper/2505.14403/) (2025)
- [Quantile Reward Policy Optimization: Alignment with Pointwise Regression and Exact Partition Functions](https://mlsanity.com/paper/2507.08068/) (2025)
- [Ratio-Variance Regularized Policy Optimization for Efficient LLM Fine-tuning](https://mlsanity.com/paper/2601.03320/) (2026)

## Abstract (arXiv)

We propose a new algorithm for fine-tuning large language models using reinforcement learning. Tapered Off-Policy REINFORCE (TOPR) uses an asymmetric, tapered variant of importance sampling to speed up learning while maintaining stable learning dynamics, even without the use of KL regularization. TOPR can be applied in a fully offline fashion, allows the handling of positive and negative examples in a unified framework, and benefits from the implementational simplicity that is typical of Monte Carlo algorithms. We demonstrate the effectiveness of our approach with a series of experiments on the GSM8K and MATH reasoning benchmarks, finding performance gains for training both a model for solution generation and as a generative verifier. We show that properly leveraging positive and negative examples alike in the off-policy regime simultaneously increases test-time accuracy and training data efficiency, all the while avoiding the ``wasted inference'' that comes with discarding negative examples. We find that this advantage persists over multiple iterations of training and can be amplified by dataset curation techniques, enabling us to match 70B-parameter model performance with 8B language models. As a corollary to this work, we find that REINFORCE's baseline parameter plays an important and unexpected role in defining dataset composition in the presence of negative examples, and is consequently critical in driving off-policy performance.