Reinforcement learning with verifiable rewards (RLVR) improves the reasoning capabilities of large language models, but prompt groups with identical rollout rewards consume generation budget without effective learning signals. Pre-rollout prompt selection can reduce this waste by screening prompts before rollout generation. However, existing pre-rollout methods struggle to balance exploitation and exploration: repeatedly exploiting historically informative prompts can narrow training coverage, whereas broader exploration can lower the fraction of informative prompts. To address these limitations, we introduce LEEPS, a Latent-Guided Explore--Exploit Prompt Sampler that adaptively balances the reuse of previously observed informative prompts with continued exploration of uncertain ones. LEEPS partitions candidates into exploit and explore portfolios and adaptively allocates rollout budget according to their recent non-trivial ratios. It further uses representation-space neighbors and historical rollout outcomes to prioritize uncertain prompts likely to yield non-zero reward variance, thereby making exploration more targeted without additional rollouts. Across six mathematical reasoning benchmarks, LEEPS achieves the highest average score at both model scales, with relative gains of 2.6\% and 3.7\% over the strongest baseline for Qwen2.5-Math-1.5B and 7B, respectively, and generally improves faster during the training process. It also achieves the highest average score across the three evaluated OOD general-reasoning benchmarks at both model scales and adds only about 2 seconds of online sampling overhead per training step. Code is available at https://github.com/ShuangLiangX/LEEPS.
Reinforcement learning (RL) finetuning significantly enhances the reasoning capabilities of large language models (LLMs), yet its effectiveness critically depends on selecting prompts of appropriate difficulty for the current policy. This is challenging because prompt difficulty evolves throughout training. Existing online methods therefore face a trade-off: evaluation-based approaches are accurate but expensive, while prediction-based approaches are efficient but typically assume stationary difficulty, making them ill-suited to RL's non-stationary training dynamics. To address these issues, we propose a Kalman-Guided Prompt Selection method (KGPS), which reformulates prompt selection as a dynamic state estimation problem rather than static difficulty prediction. KGPS models each prompt's latent success rate in logit space using a linear-Gaussian state-space model, with process noise coupled to the magnitude of policy updates so that uncertainty increases when the policy changes more substantially. A Kalman filter then maintains a calibrated Gaussian posterior over prompt difficulty, and prompts are selected by maximizing a posterior-expected training utility that favors intermediate-difficulty prompts while naturally revisiting uncertain ones. The resulting procedure is adaptive to policy drift and requires no additional rollouts beyond standard policy training. Extensive experiments across mathematics, planning, and geometry reasoning benchmarks, as well as multiple RL algorithms, show that KGPS consistently improves both final accuracy and rollout efficiency over strong baselines, establishing state-of-the-art performance among online prompt selection methods. For example, on DeepSeek-R1-Distill-7B, KGPS uses 83% fewer rollouts than DS while even improving the average performance by 0.12 point across six math reasoning benchmarks.