# RAPID: An Efficient Reinforcement Learning Algorithm for Small Language Models

arXiv: https://arxiv.org/abs/2510.03515 · HTML: https://mlsanity.com/paper/2510.03515/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 32 references that are in the map.
- First posted on arXiv 3 Oct 2025.

## Builds on (most cited first, 24 of 24)

- [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)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [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)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Is Your Code Generated by ChatGPT Really Correct? Rigorous Evaluation of Large Language Models for Code Generation](https://mlsanity.com/paper/2305.01210/) (2023)
- [ZeRO: Memory Optimizations Toward Training Trillion Parameter Models](https://mlsanity.com/paper/1910.02054/) (2019)
- [Graph of Thoughts: Solving Elaborate Problems with Large Language Models](https://mlsanity.com/paper/2308.09687/) (2023)
- [IMPALA: Scalable Distributed Deep-RL with Importance Weighted Actor-Learner Architectures](https://mlsanity.com/paper/1802.01561/) (2018)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [MiniF2F: a cross-system benchmark for formal Olympiad-level mathematics](https://mlsanity.com/paper/2109.00110/) (2021)
- [AgentTuning: Enabling Generalized Agent Abilities for LLMs](https://mlsanity.com/paper/2310.12823/) (2023)
- [FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI](https://mlsanity.com/paper/2411.04872/) (2024)
- [CodeNet: A Large-Scale AI for Code Dataset for Learning a Diversity of Coding Tasks](https://mlsanity.com/paper/2105.12655/) (2021)
- [Evaluating the Diversity and Quality of LLM Generated Content](https://mlsanity.com/paper/2504.12522/) (2025)
- [Reducing Variance in Temporal-Difference Value Estimation via Ensemble of Deep Networks](https://mlsanity.com/paper/2209.07670/) (2022)

## Built on by (most cited first, 1 of 1)

- [CoFineLLM: Conformal Finetuning of LLMs for Language-Instructed Robot Planning](https://mlsanity.com/paper/2511.06575/) (2025)

## Abstract (arXiv)

Reinforcement learning (RL) has emerged as a promising strategy for finetuning small language models (SLMs) to solve targeted tasks such as math and coding. However, RL algorithms tend to be resource-intensive, taking a significant amount of time to train. We propose RAPID, a novel RL algorithm that can substantially reduce the running time of RL. Our key insight is that RL tends to be costly due to the need to perform both inference and backpropagation during training. To maximize use of computational resources, our algorithm performs inference in large batches, and then performs off-policy policy gradient updates in mini-batches. For off-policy updates, we incorporate group advantage estimation into the policy gradient algorithm, and derive an importance weighted estimator to correct for the bias arising from off-policy learning. Our experiments demonstrate that our algorithm can reduce running time by 11%-34% on three benchmarks compared to state-of-the-art RL algorithms while maintaining similar or better accuracy.