Rethinking the Sampling Criteria in Reinforcement Learning for LLM Reasoning: A Competence-Difficulty Alignment Perspective

TL;DR

This paper proposes CDAS, a novel sampling method for reinforcement learning in large language models that improves reasoning accuracy and efficiency by aligning problem difficulty with model competence using historical performance data.

Contribution

It introduces a competence-difficulty alignment sampling method that provides stable difficulty estimation and adaptive problem selection based on model competence.

Findings

CDAS achieves higher accuracy than baseline methods.

CDAS significantly improves training efficiency.

CDAS is 2.33 times faster than the Dynamic Sampling strategy.

Abstract

Reinforcement learning exhibits potential in enhancing the reasoning abilities of large language models, yet it is hard to scale for the low sample efficiency during the rollout phase. Existing methods attempt to improve efficiency by scheduling problems based on problem difficulties. However, these approaches suffer from unstable and biased estimations of problem difficulty and fail to capture the alignment between model competence and problem difficulty in RL training, leading to suboptimal results. To tackle these limitations, this paper introduces $\textbf{C}$ompetence-$\textbf{D}$ifficulty $\textbf{A}$lignment $\textbf{S}$ampling ($\textbf{CDAS}$), which enables accurate and stable estimation of problem difficulties by aggregating historical performance discrepancies of problems. Then the model competence is quantified to adaptively select problems whose difficulty is in alignment with the model's current competence using a fixed-point system. Experimental results across a range of challenging mathematical benchmarks show that CDAS achieves great improvements in both accuracy and efficiency. CDAS attains the highest average accuracy against baselines and exhibits significant speed advantages compared to Dynamic Sampling, a competitive strategy in DAPO, which is 2.33 times slower than CDAS.