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

TL;DR

This work tackles the low sample efficiency of reinforcement learning for enhancing LLM reasoning by critiquing traditional difficulty proxies like single-step pass rates. It introduces Competence-Difficulty Alignment Sampling (CDAS), which models problem difficulty as a trajectory of historical performance discrepancies and uses a fixed-point system to align this difficulty with the model's competence for adaptive sampling. Empirical results on diverse mathematical benchmarks show that CDAS achieves the highest average accuracy while significantly reducing training time compared to Dynamic Sampling, and it demonstrates strong gains on harder tasks such as AIME25. The method also generalizes to code generation and larger LLMs, underscoring the practical impact of dynamically matching problem difficulty to model competence in RL-based reasoning.

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.

Figures (14)

• Figure 1: Average accuracy (left) and training GPU hours (right) of different sampling strategies.
• Figure 2: The variation in pass rate of problems in palin GRPO on Qwen-2.5 7Byang2024qwen2p5 using MATH dataset.
• Figure 3: Pass Rate vs Step.
• Figure 4: Training curves of different sampling strategies.
• Figure 5: Ablation study of the warm-up phase