# Step-wise Adaptive Integration of Supervised Fine-tuning and Reinforcement Learning for Task-Specific LLMs

arXiv: https://arxiv.org/abs/2505.13026 · HTML: https://mlsanity.com/paper/2505.13026/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 28 of its 37 references that are in the map.
- First posted on arXiv 19 May 2025.

## Placed in

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

## Builds on (most cited first, 28 of 28)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [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)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [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)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Graph of Thoughts: Solving Elaborate Problems with Large Language Models](https://mlsanity.com/paper/2308.09687/) (2023)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [Large Language Models for Mathematical Reasoning: Progresses and Challenges](https://mlsanity.com/paper/2402.00157/) (2024)
- [Logic-RL: Unleashing LLM Reasoning with Rule-Based Reinforcement Learning](https://mlsanity.com/paper/2502.14768/) (2025)
- [ReFT: Reasoning with Reinforced Fine-Tuning](https://mlsanity.com/paper/2401.08967/) (2024)
- [Does Fine-Tuning LLMs on New Knowledge Encourage Hallucinations?](https://mlsanity.com/paper/2405.05904/) (2024)
- [The Unreliability of Explanations in Few-shot Prompting for Textual Reasoning](https://mlsanity.com/paper/2205.03401/) (2022)
- [Teaching Large Language Models to Reason with Reinforcement Learning](https://mlsanity.com/paper/2403.04642/) (2024)
- [Language Models Learn to Mislead Humans via RLHF](https://mlsanity.com/paper/2409.12822/) (2024)
- [Q*: Improving Multi-step Reasoning for LLMs with Deliberative Planning](https://mlsanity.com/paper/2406.14283/) (2024)
- [Inverse-RLignment: Large Language Model Alignment from Demonstrations through Inverse Reinforcement Learning](https://mlsanity.com/paper/2405.15624/) (2024)
- [Disperse-Then-Merge: Pushing the Limits of Instruction Tuning via Alignment Tax Reduction](https://mlsanity.com/paper/2405.13432/) (2024)
- [Investigating Mysteries of CoT-Augmented Distillation](https://mlsanity.com/paper/2406.14511/) (2024)

## Built on by (most cited first, 25 of 25)

- [On-Policy RL Meets Off-Policy Experts: Harmonizing Supervised Fine-Tuning and Reinforcement Learning via Dynamic Weighting](https://mlsanity.com/paper/2508.11408/) (2025)
- [SRFT: A Single-Stage Method with Supervised and Reinforcement Fine-Tuning for Reasoning](https://mlsanity.com/paper/2506.19767/) (2025)
- [Blending Supervised and Reinforcement Fine-Tuning with Prefix Sampling](https://mlsanity.com/paper/2507.01679/) (2025)
- [RL-PLUS: Countering Capability Boundary Collapse of LLMs in Reinforcement Learning with Hybrid-policy Optimization](https://mlsanity.com/paper/2508.00222/) (2025)
- [Asymmetric On-Policy Distillation: Bridging Exploitation and Imitation at the Token Level](https://mlsanity.com/paper/2605.06387/) (2026)
- [RL Squeezes, SFT Expands: A Comparative Study of Reasoning LLMs](https://mlsanity.com/paper/2509.21128/) (2025)
- [Beyond Two-Stage Training: Cooperative SFT and RL for LLM Reasoning](https://mlsanity.com/paper/2509.06948/) (2025)
- [Adaptive Rollout Allocation for Online Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2602.01601/) (2026)
- [Mitigating Forgetting Between Supervised and Reinforcement Learning Yields Stronger Reasoners](https://mlsanity.com/paper/2510.04454/) (2025)
- [CORRECT: COndensed eRror RECognition via knowledge Transfer in multi-agent systems](https://mlsanity.com/paper/2509.24088/) (2025)
- [SFT-then-RL Outperforms Mixed-Policy Methods for LLM Reasoning](https://mlsanity.com/paper/2604.23747/) (2026)
- [EvoCoT: Overcoming the Exploration Bottleneck in Reinforcement Learning](https://mlsanity.com/paper/2508.07809/) (2025)
- [When RL Fails after SFT: Rejuvenating Model Plasticity for Robust SFT-to-RL Handoff](https://mlsanity.com/paper/2606.09932/) (2026)
- [Recall-Extend Dynamics: Enhancing Small Language Models through Controlled Exploration and Refined Offline Integration](https://mlsanity.com/paper/2508.16677/) (2025)
- [Rethinking Large Language Model Distillation: A Constrained Markov Decision Process Perspective](https://mlsanity.com/paper/2509.22921/) (2025)
- [Toward Honest Language Models for Deductive Reasoning](https://mlsanity.com/paper/2511.09222/) (2025)
- [Gradients Must Earn Their Influence: Unifying SFT with Generalized Entropic Objectives](https://mlsanity.com/paper/2602.11424/) (2026)
- [Supervised Fine-Tuning versus Reinforcement Learning: A Study of Post-Training Methods for Large Language Models](https://mlsanity.com/paper/2603.13985/) (2026)
- [GIFT: Reconciling Post-Training Objectives via Variational Finite-Temperature Gibbs Initialization](https://mlsanity.com/paper/2601.09233/) (2026)
- [Learning to Search: A Decision-Based Agent for Knowledge-Based Visual Question Answering](https://mlsanity.com/paper/2604.07146/) (2026)
- [KEPO: Knowledge-Enhanced Preference Optimization for Multimodal Reasoning with Applications to Medical VQA](https://mlsanity.com/paper/2602.00400/) (2026)
- [AnE: Pushing the Reasoning Frontier of Multimodal LLMs via Anchor Evolution](https://mlsanity.com/paper/2605.25571/) (2026)
- [Boosting Reinforcement Learning with Verifiable Rewards via Randomly Selected Few-Shot Guidance](https://mlsanity.com/paper/2605.15012/) (2026)
- [MERGED: Multimodal Entity Resolution via Generated Expert Reasoning Distillation](https://mlsanity.com/paper/2609.01913/) (2026)
- [The Weakest Link: Distilling LLM Reasoning with Worst-Case Constrained Reinforcement Learning](https://mlsanity.com/paper/2610.00332/) (2026)

## Abstract (arXiv)

Large language models (LLMs) excel at mathematical reasoning and logical problem-solving. The current popular training paradigms primarily use supervised fine-tuning (SFT) and reinforcement learning (RL) to enhance the models' reasoning abilities. However, when using SFT or RL alone, there are respective challenges: SFT may suffer from overfitting, while RL is prone to mode collapse. The state-of-the-art methods have proposed hybrid training schemes. However, static switching faces challenges such as poor generalization across different tasks and high dependence on data quality. In response to these challenges, inspired by the curriculum learning-quiz mechanism in human reasoning cultivation, We propose SASR, a step-wise adaptive hybrid training framework that theoretically unifies SFT and RL and dynamically balances the two throughout optimization. SASR uses SFT for initial warm-up to establish basic reasoning skills, and then uses an adaptive dynamic adjustment algorithm based on gradient norm and divergence relative to the original distribution to seamlessly integrate SFT with the online RL method GRPO. By monitoring the training status of LLMs and adjusting the training process in sequence, SASR ensures a smooth transition between training schemes, maintaining core reasoning abilities while exploring different paths. Experimental results demonstrate that SASR outperforms SFT, RL, and static hybrid training methods.