Reinforcement Learning with Verifiable Rewards (RLVR) has become an effective post-training paradigm for improving the reasoning abilities of large language models. However, existing RLVR methods typically rely on final-answer correctness to assign trajectory-level rewards, providing sparse supervision and treating all tokens uniformly regardless of their actual contribution to reasoning. Although recent studies introduce intermediate signals such as process rewards, high-entropy tokens, and semantic uncertainty, these signals are often not inherently verifiable and may fail to distinguish beneficial strategic patterns from harmful ones. To address this limitation, we propose STRIDE (Strategic Trajectory Reasoning with Discriminative Estimation), a fine-grained RLVR framework that derives strategic reasoning supervision from verifiable outcomes. STRIDE contrasts successful and failed trajectories within each response group to estimate the outcome-discriminative preference of each $n$-gram strategic pattern, and further combines this signal with reasoning saliency entropy to identify decision-relevant strategic patterns. These patterns are assigned differentiated advantage values during RL optimization, enabling more precise credit assignment while preserving the verifiability of RLVR. Extensive experiments demonstrate that STRIDE consistently improves reasoning performance across diverse models, tasks, and extended settings, including VLMs and agent-based systems.

翻译：摘要：可验证奖励强化学习（RLVR）已成为提升大型语言模型推理能力的有效后训练范式。然而，现有RLVR方法通常仅依据最终答案正确性分配轨迹级奖励，这种稀疏监督机制对所有词元一视同仁，忽略了其对推理过程的实际贡献。尽管近期研究引入了过程奖励、高熵词元和语义不确定性等中间信号，但这些信号往往不具备内在可验证性，且难以区分有益策略模式与有害模式。为解决这一局限，我们提出STRIDE（基于判别式估计的策略轨迹推理）——一种从可验证结果中提取策略推理监督信号的细粒度RLVR框架。STRIDE通过对比各组响应中的成功轨迹与失败轨迹，估算每条n-gram策略模式的结果判别偏好，并将此信号与推理显著熵相结合，识别与决策相关的策略模式。在强化学习优化过程中，这些模式被赋予差异化的优势值，从而在保持RLVR可验证性的同时实现更精准的信度分配。大量实验表明，STRIDE在各类模型、任务及扩展场景（包括视觉语言模型和基于智能体的系统）中均能持续提升推理性能。