# Selective-Advantage Entropy-Adaptive Horizon GRPO: Asymmetric Token-Level Discounting for Efficient Reinforcement Learning of Language Models

arXiv: https://arxiv.org/abs/2606.05434 · HTML: https://mlsanity.com/paper/2606.05434/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 12 of its 16 references that are in the map.
- First posted on arXiv 3 Jun 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)
- LLM alignment / RLHF / preference optimisation / [Process reward models for reasoning](https://mlsanity.com/alignment/process-reward-models-for-reasoning/)

## Builds on (most cited first, 12 of 12)

- [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)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [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)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Advancing LLM Reasoning Generalists with Preference Trees](https://mlsanity.com/paper/2404.02078/) (2024)
- [Aligning Large Language Models via Fine-grained Supervision](https://mlsanity.com/paper/2406.02756/) (2024)

## Abstract (arXiv)

Group Relative Policy Optimisation (GRPO) has emerged as an effective reinforcement-learning algorithm for aligning language models on reasoning tasks, but it treats every token position and every sampled rollout symmetrically. We introduce two complementary extensions: (i) Adaptive-Horizon GRPO (AH-GRPO), which weights each token's policy gradient using a cumulative entropy-based discount that reduces the effective horizon when the model is uncertain, and (ii) Selective-Advantage AH-GRPO (SA-AH-GRPO), which applies this discounting only to negative-advantage rollouts, leaving positive-advantage, successful trajectories unattenuated. We evaluate standard GRPO with alpha = 0, AH-GRPO with alpha = 0.5, and SA-AH-GRPO with alpha = 0.5 on the GSM8K mathematical reasoning benchmark using both Qwen 2.5-1.5B-Instruct and Qwen 2.5-3B-Instruct fine-tuned with LoRA. On the 3B model, SA-AH-GRPO achieves Pass@1 = 0.858 at its peak at step 30 and maintains 0.846 at 180 steps, with training variance reduced to 0.0246, a 3.6 times reduction relative to GRPO while matching its peak accuracy. On the 1.5B model, SA-AH-GRPO achieves a peak Pass@1 of 0.686, improving over the zero-shot baseline of 0.637. Our analysis shows that asymmetric discounting preserves the full gradient signal on correct solutions, prevents entropy collapse, and substantially stabilises training, suggesting a principled inductive bias for reinforcement learning with verifiable rewards on structured generation tasks.