# HAPO: Training Language Models to Reason Concisely via History-Aware Policy Optimization

arXiv: https://arxiv.org/abs/2505.11225 · HTML: https://mlsanity.com/paper/2505.11225/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 41 of its 47 references that are in the map.
- First posted on arXiv 16 May 2025.

## Placed in

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

## Builds on (most cited first, 30 of 41)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Graph of Thoughts: Solving Elaborate Problems with Large Language Models](https://mlsanity.com/paper/2308.09687/) (2023)
- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs](https://mlsanity.com/paper/2412.21187/) (2024)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [Stop Overthinking: A Survey on Efficient Reasoning for Large Language Models](https://mlsanity.com/paper/2503.16419/) (2025)
- [Training Language Models to Self-Correct via Reinforcement Learning](https://mlsanity.com/paper/2409.12917/) (2024)
- [Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach](https://mlsanity.com/paper/2502.05171/) (2025)
- [L1: Controlling How Long A Reasoning Model Thinks With Reinforcement Learning](https://mlsanity.com/paper/2503.04697/) (2025)
- [Demystifying Long Chain-of-Thought Reasoning in LLMs](https://mlsanity.com/paper/2502.03373/) (2025)
- [Chain of Draft: Thinking Faster by Writing Less](https://mlsanity.com/paper/2502.18600/) (2025)
- [O1-Pruner: Length-Harmonizing Fine-Tuning for O1-Like Reasoning Pruning](https://mlsanity.com/paper/2501.12570/) (2025)
- [TokenSkip: Controllable Chain-of-Thought Compression in LLMs](https://mlsanity.com/paper/2502.12067/) (2025)
- [Token-Budget-Aware LLM Reasoning](https://mlsanity.com/paper/2412.18547/) (2024)
- [Training Language Models to Reason Efficiently](https://mlsanity.com/paper/2502.04463/) (2025)
- [Making Large Language Models Better Reasoners with Step-Aware Verifier](https://mlsanity.com/paper/2206.02336/) (2022)
- [CODI: Compressing Chain-of-Thought into Continuous Space via Self-Distillation](https://mlsanity.com/paper/2502.21074/) (2025)

## Built on by (most cited first, 19 of 19)

- [Don't Overthink It: A Survey of Efficient R1-style Large Reasoning Models](https://mlsanity.com/paper/2508.02120/) (2025)
- [Towards Concise and Adaptive Thinking in Large Reasoning Models: A Survey](https://mlsanity.com/paper/2507.09662/) (2025)
- [DRPO: Efficient Reasoning via Decoupled Reward Policy Optimization](https://mlsanity.com/paper/2510.04474/) (2025)
- [On-policy Distillation with Verifiable Reward](https://mlsanity.com/paper/2608.24696/) (2026)
- [LAPO: Internalizing Reasoning Efficiency via Length-Adaptive Policy Optimization](https://mlsanity.com/paper/2507.15758/) (2025)
- [Hierarchical Budget Policy Optimization for Adaptive Reasoning](https://mlsanity.com/paper/2507.15844/) (2025)
- [Probing the Difficulty Perception Mechanism of Large Language Models](https://mlsanity.com/paper/2510.05969/) (2025)
- [LACONIC: Length-Aware Constrained Reinforcement Learning for LLM](https://mlsanity.com/paper/2602.14468/) (2026)
- [Can Confidence Estimates Decide When Chain-of-Thought Is Necessary for LLMs?](https://mlsanity.com/paper/2510.21007/) (2025)
- [QA-Merging: Query-Adaptive Reasoning via Layer Selective Model Merging](https://mlsanity.com/paper/2601.03506/) (2026)
- [MathMixup: Boosting LLM Mathematical Reasoning with Difficulty-Controllable Data Synthesis and Curriculum Learning](https://mlsanity.com/paper/2601.17006/) (2026)
- [Reasoning as Compression: Unifying Budget Forcing via the Conditional Information Bottleneck](https://mlsanity.com/paper/2603.08462/) (2026)
- [Revisiting Reinforcement Learning with Verifiable Rewards from a Contrastive Perspective](https://mlsanity.com/paper/2605.12969/) (2026)
- [ENTRA: Entropy-Based Redundancy Avoidance in Large Language Model Reasoning](https://mlsanity.com/paper/2601.07123/) (2026)
- [Efficient Reasoning on the Edge](https://mlsanity.com/paper/2603.16867/) (2026)
- [Avoiding Overthinking and Underthinking: Curriculum-Aware Budget Scheduling for LLMs](https://mlsanity.com/paper/2604.19780/) (2026)
- [LEAD: Length-Efficient Adaptive and Dynamic Reasoning for Large Language Models](https://mlsanity.com/paper/2605.09806/) (2026)
- [Decomposer: Learning to Decompile Symbolic Music to Programs](https://mlsanity.com/paper/2607.01849/) (2026)
- [Efficient Reasoning Training Does Not Always Harm CoT Faithfulness and Monitorability](https://mlsanity.com/paper/2610.03509/) (2026)

## Abstract (arXiv)

While scaling the length of responses at test-time has been shown to markedly improve the reasoning abilities and performance of large language models (LLMs), it often results in verbose outputs and increases inference cost. Prior approaches for efficient test-time scaling, typically using universal budget constraints or query-level length optimization, do not leverage historical information from previous encounters with the same problem during training. We hypothesize that this limits their ability to progressively make solutions more concise over time. To address this, we present History-Aware Policy Optimization (HAPO), which keeps track of a history state (e.g., the minimum length over previously generated correct responses) for each problem. HAPO employs a novel length reward function based on this history state to incentivize the discovery of correct solutions that are more concise than those previously found. Crucially, this reward structure avoids overly penalizing shorter incorrect responses with the goal of facilitating exploration towards more efficient solutions. By combining this length reward with a correctness reward, HAPO jointly optimizes for correctness and efficiency. We use HAPO to train DeepSeek-R1-Distill-Qwen-1.5B, DeepScaleR-1.5B-Preview, and Qwen-2.5-1.5B-Instruct, and evaluate HAPO on several math benchmarks that span various difficulty levels. Experiment results demonstrate that HAPO effectively induces LLMs' concise reasoning abilities, producing length reductions of 33-59% with accuracy drops of only 2-5%.