# LLMs Can Learn to Reason Via Off-Policy RL

arXiv: https://arxiv.org/abs/2602.19362 · HTML: https://mlsanity.com/paper/2602.19362/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 34 of its 50 references that are in the map.
- First posted on arXiv 22 Feb 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

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

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Dota 2 with Large Scale Deep Reinforcement Learning](https://mlsanity.com/paper/1912.06680/) (2019)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [IMPALA: Scalable Distributed Deep-RL with Importance Weighted Actor-Learner Architectures](https://mlsanity.com/paper/1802.01561/) (2018)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [DeepSeek-V3.2: Pushing the Frontier of Open Large Language Models](https://mlsanity.com/paper/2512.02556/) (2025)
- [Kimi K2: Open Agentic Intelligence](https://mlsanity.com/paper/2507.20534/) (2025)
- [Safe and Efficient Off-Policy Reinforcement Learning](https://mlsanity.com/paper/1606.02647/) (2016)
- [AReaL: A Large-Scale Asynchronous Reinforcement Learning System for Language Reasoning](https://mlsanity.com/paper/2505.24298/) (2025)
- [Sample Efficient Actor-Critic with Experience Replay](https://mlsanity.com/paper/1611.01224/) (2016)
- [The Art of Scaling Reinforcement Learning Compute for LLMs](https://mlsanity.com/paper/2510.13786/) (2025)
- [Asynchronous RLHF: Faster and More Efficient Off-Policy RL for Language Models](https://mlsanity.com/paper/2410.18252/) (2024)
- [Defeating the Training-Inference Mismatch via FP16](https://mlsanity.com/paper/2510.26788/) (2025)
- [Tapered Off-Policy REINFORCE: Stable and efficient reinforcement learning for LLMs](https://mlsanity.com/paper/2503.14286/) (2025)
- [Prosperity before Collapse: How Far Can Off-Policy RL Reach with Stale Data on LLMs?](https://mlsanity.com/paper/2510.01161/) (2025)
- [Offline Regularised Reinforcement Learning for Large Language Models Alignment](https://mlsanity.com/paper/2405.19107/) (2024)
- [Klear-Reasoner: Advancing Reasoning Capability via Gradient-Preserving Clipping Policy Optimization](https://mlsanity.com/paper/2508.07629/) (2025)
- [Revisiting Design Choices in Proximal Policy Optimization](https://mlsanity.com/paper/2009.10897/) (2020)
- [Regressing the Relative Future: Efficient Policy Optimization for Multi-turn RLHF](https://mlsanity.com/paper/2410.04612/) (2024)
- [Asymmetric REINFORCE for off-Policy Reinforcement Learning: Balancing positive and negative rewards](https://mlsanity.com/paper/2506.20520/) (2025)
- [Accelerating RL for LLM Reasoning with Optimal Advantage Regression](https://mlsanity.com/paper/2505.20686/) (2025)
- [Generalized Emphatic Temporal Difference Learning: Bias-Variance Analysis](https://mlsanity.com/paper/1509.05172/) (2015)
- [Emphatic Temporal-Difference Learning](https://mlsanity.com/paper/1507.01569/) (2015)
- [Qsharp: Provably Optimal Distributional RL for LLM Post-Training](https://mlsanity.com/paper/2502.20548/) (2025)

## Built on by (most cited first, 10 of 10)

- [Lightning OPD: Efficient Post-Training for Large Reasoning Models with Offline On-Policy Distillation](https://mlsanity.com/paper/2604.13010/) (2026)
- [Agentic Aggregation for Parallel Scaling of Long-Horizon Agentic Tasks](https://mlsanity.com/paper/2604.11753/) (2026)
- [REGEN: Replay-recycling for Expert-to-Generalist distillation with Offline Reinforcement Learning](https://mlsanity.com/paper/2607.19450/) (2026)
- [JigsawRL: Assembling RL Pipelines for Efficient LLM Post-Training](https://mlsanity.com/paper/2604.23838/) (2026)
- [Reusing Rollouts under Policy Lag: Prefix-Normalized Policy Optimization for LLM Reinforcement Learning](https://mlsanity.com/paper/2608.01418/) (2026)
- [Off-Policy Value-Based Reinforcement Learning for Large Language Models](https://mlsanity.com/paper/2603.23355/) (2026)
- [Apriel-Reasoner: RL Post-Training for General-Purpose and Efficient Reasoning](https://mlsanity.com/paper/2604.02007/) (2026)
- [BRACE: Anchored Bellman-Residual Correction for Stale Critics in Asynchronous RL](https://mlsanity.com/paper/2609.09783/) (2026)
- [MInTRL: Off-policy Intervention can boost On-policy RL](https://mlsanity.com/paper/2609.12419/) (2026)
- [Asynchronous LLM Post-Training: Group-Mass Capping and Convergence Analysis](https://mlsanity.com/paper/2610.01896/) (2026)

## Abstract (arXiv)

Reinforcement learning (RL) approaches for Large Language Models (LLMs) frequently use on-policy algorithms, such as PPO or GRPO. However, policy lag from distributed training architectures and differences between the training and inference policies break this assumption, making the data off-policy by design. To rectify this, prior work has focused on making this off-policy data appear more on-policy, either via importance sampling (IS), or by more closely aligning the training and inference policies by explicitly modifying the inference engine. In this work, we embrace off-policyness and propose a novel off-policy RL algorithm that does not require these modifications: Optimal Advantage-based Policy Optimization with Lagged Inference policy (OAPL). We show that OAPL outperforms GRPO with importance sampling on competition math benchmarks, and can match the performance of a publicly available coding model, DeepCoder, on LiveCodeBench, while using 3x fewer generations during training. We further empirically demonstrate that models trained via OAPL have improved test time scaling under the Pass@k metric. OAPL allows for efficient, effective post-training even with lags of more than 400 gradient steps between the training and inference policies, 100x more off-policy than prior approaches.