Predictive Bandit Curriculum Reinforcement Learning via Gradient-Based Sample Group Discovery

Measuring learning progress is essential for curiosity-driven exploration in reinforcement learning, but widely used signals such as prediction error often fail to distinguish meaningful, learnable patterns from random noise. This paper proposes Gradient-Momentum Coupling (GMC), a signal derived from optimization dynamics that quantifies how useful each sample's gradient is for ongoing learning by measuring its per-parameter normalized absolute product with the momentum from previous gradients. By leveraging momentum's natural filtering of noise and oscillations, GMC identifies samples that contribute to ongoing parameter updates. Controlled experiments demonstrate noise robustness and emergent curriculum learning, with the signal prioritizing tasks by learning speed rather than difficulty. Experiments on MiniGrid suggest that replacing prediction error with GMC within existing curiosity-driven architectures can improve robustness to observation noise.

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.

We introduce Predictive Batch Scheduling (PBS), a novel training optimization technique that accelerates language model convergence by dynamically prioritizing high-loss samples during batch construction. Unlike curriculum learning approaches that require predefined difficulty metrics or hard example mining methods that demand expensive per-sample loss tracking, PBS employs a lightweight linear predictor trained online to estimate sample difficulty from static token-level features. Our predictor achieves 0.44 correlation with actual loss using only four simple features: token frequency, sequence length, vocabulary diversity, and rare token ratio. Experiments on a 130M parameter transformer demonstrate that PBS achieves 6-13% faster convergence measured by evaluation loss across training checkpoints, with the predictor's correlation improving from 0.14 to 0.44 over 10,000 training steps. These results validate that token frequency statistics encode meaningful information about sample difficulty, enabling effective curriculum learning with negligible computational overhead.