流形赌博机:基于大语言模型潜在几何结构的贝叶斯课程学习
阅读原文· arxiv.org强化学习中,问题采样策略对提升大语言模型(LLM)推理能力至关重要。现有自适应课程学习方法将问题选择视为独立臂的赌博机问题,忽略了任务空间的结构化异质性。本文提出贝叶斯流形课程(BMC),将问题采样建模为流形结构的非平稳赌博机,利用层次任务树和贝叶斯学习引导采样。实验表明,不同采样策略在生产率、多样性和效用间存在权衡,仅优先难度不足以实现强下游性能。
Reinforcement learning (RL) is a central approach for improving reasoning capabilities in large language models (LLMs), where training efficiency depends critically on how problems are sampled during optimization. Existing adaptive curriculum learning methods typically prioritize prompts of intermediate difficulty, treating problem selection as a standard bandit problem with independent arms and overlooking the structured, heterogeneous nature of the task space. In this work, we frame problem sampling as a manifold-structured bandit problem with endogenous non-stationarity: problems are related through the model's latent representation space, and sampling decisions can steer how learning signals evolve across that space. To operationalize this perspective, we introduce Bayesian Manifold Curriculum (BMC), a structure-aware framework that organizes problems into a hierarchical task tree and applies Bayesian learning to guide sampling. Empirically, we find that different sampling strategies induce non-trivial tradeoffs between productivity (learning signal), diversity (coverage of the task manifold), and utility (evaluation relevance). These results show that prioritizing difficulty alone is insufficient for strong downstream performance, highlighting the importance of incorporating structure and type-awareness into problem sampling.