From Trial-and-Error to Improvement: A Systematic Analysis of LLM Exploration Mechanisms in RLVR

Reinforcement learning with verifiable rewards (RLVR) has emerged as a powerful paradigm for enhancing the reasoning capabilities of large language models (LLMs). Unlike traditional RL approaches, RLVR leverages rule-based feedback to guide LLMs in generating and refining complex reasoning chains—a process critically dependent on effective exploration strategies. While prior work has demonstrated RLVR’s empirical success, the fundamental mechanisms governing LLMs’ exploration behaviors remain underexplored. This technical report presents a systematic investigation of exploration capacities in RLVR, covering four main aspects: (1) exploration space shaping, where we develop quantitative metrics to characterize LLMs’ capability boundaries; (2) entropy-performance exchange, analyzed across training stages, individual instances, and token-level patterns; and (3) RL performance optimization, examining methods to effectively translate exploration gains into measurable improvements. By unifying previously identified insights with new empirical evidence, this work aims to provide a foundational framework for advancing RLVR systems.

In RLVR, LLMs first generate rollout responses to training problem prompts and then leverage these self-generated responses to improve model performance. This learning process iterates until performance gains become negligible. A crucial aspect of RLVR is enabling effective exploration within the vast state space of natural language. Research [7] has shown that the exploration capabilities of LLMs not only influence immediate learning progress but also determine the ultimate performance of the models. Thus, developing a systematic understanding of LLMs’ exploration abilities—and how they drive performance improvements—is essential for RLVR.

To investigate the exploration mechanism in RLVR, we first revisit the fundamental exploration-exploitation trade-off in the classic RL literature [8]. An RL agent must strategically balance exploration (testing novel actions to discover improved strategies) and exploitation (leveraging known optimal actions to earn immediate rewards). This balance is crucial: excessive exploration delays convergence, while insufficient exploration may lead to locally optimal but globally subpar policies. In RLVR, verifiable rewards enable LLMs to guide their exploration in a task-aligned manner. The framework uses exploratory actions to identify potentially correct solutions to reasoning tasks, then reinforces successful solutions while pruning unsuccessful attempts—creating a self-improving cycle of reasoning refinement.

Given the pivotal role of exploration mechanisms in RLVR, this domain has drawn considerable research interest, spanning investigations of entropy mechanisms [9, 7] (where entropy reduction enhances performance) to various enhancement techniques [10, 11] (e.g., Clip-higher). However, despite these advances, current studies have predominantly examined either isolated or coarsegrained aspects of exploration mechanisms. A comprehensive understanding of several fundamental issues remains lacking, particularly regarding how to properly structure the exploration space, how exploration precisely translates to performance gains, and how to effectively augment exploration capabilities.

In this technical report, we conduct a systematic investigation of the fundamental exploration mechanisms employed by LLMs in RLVR. Our methodology integrates a comprehensive literature review with rigorous empirical analysis. The discussion is organized around three key dimensions:

• Exploration space structure (Section 2): We investigate methods to structure the exploration space for LLMs, with particular focus on developing quantitative metrics to characterize their capability boundaries. This involves determining both the solvable and unsolvable problems within practical LLM rollout constraints. Furthermore, we also compare how two primary post-training approaches—SFT and RL—influence LLM exploration capabilities and overall performance.

• Entropy-performance interplay (Section 3): We investigate the relationship between entropy (a key indicator of exploration capability) and model performance. Our analysis extends beyond reviewing recent advances in this area to include a multi-granularity empirical examination across three levels: stage-level dynamics, instance-level efficiency, and token-level significance.

• Performance improvement (Section 4): We discuss approaches to enhancing reasoning abilities, with a particular focus on two main aspects: (1) expanding exploration capacities and (2) enhancing the performance conversion efficacy. Concretely, we first review recent advancements in strengthening the exploration abilities of LLMs. Moreover, we conduct experiments to investigate how to preserve Pass@k performance during training and propose two simple methods to boost the RL efficiency.