Learning from Hard Prompts: Difficulty-aware Advantage Amplification in Dynamic Sampling

2026-08-28

AI Summary

本文提出Direct Advantage Amplification方法，解决Dynamic Sampling在处理难样本时训练效率低的问题，通过放大难样本中正确响应的优势，提高训练效率。

Abstract

Decoupled Clip and Dynamic Sampling Policy Optimization (DAPO) is a prominent variant of Group Relative Policy Optimization (GRPO). DAPO introduces several improvements over GRPO. Among these, Dynamic Sampling contributes the most to DAPO's accuracy gains relative to GRPO. To improve accuracy, Dynamic Sampling enhances training stability by eliminating zero policy gradients from zero advantages. Specifically, it avoids such zero gradients by filtering out prompts where sampled responses are either entirely correct or incorrect. However, our theoretical analysis shows that Dynamic Sampling decrease training efficiency as it cannot effectively utilize hard-to-sample correct responses on hard prompts. Formally, it asymmetrically amplifies the advantages of distinct responses to the same prompts. On hard prompts, incorrect responses undergo greater amplification than correct ones. This leads the model to avoid generating the observed incorrect responses rather than capitalizing on the hard-to-sample correct ones on hard prompts, resulting in low training efficiency. To improve training efficiency, we propose Direct Advantage Amplification (DAA), which amplifies the advantages of hard-to-sample correct responses on hard prompts, as obtained by Dynamic Sampling. This ensures that, when Dynamic Sampling is used, these hard-to-sample responses can be effectively capitalized on, implying higher training efficiency. By integrating DAA into DAPO, we obtain Difficulty-aware Advantage Amplification Policy Optimization (DA3PO), which is implemented with fewer than 30 lines of code from DAPO. Experiments show that DA3PO significantly outperforms GRPO and other classical GRPO variants.

Problem

• Dynamic Sampling
• Training Efficiency
• Hard Prompts

Innovation

• Direct Advantage Amplification
• Dynamic Sampling
• Hard Prompts
• Training Efficiency