DeepSeek-R1-Distill-Qwen-1.5B上，LSPO用LoRA支架捡回GRPO在零奖励提示上的梯度，比DAPO平均高3.8个点。
数学推理的RLVR存在盲区：当一组采样全部失败时，GRPO的优势函数为零，导致模型在能力边界提示上无梯度。LSPO在每个RL步检测这类悬崖提示，用其标准答案快速拟合一个小型LoRA适配器，然后重新采样并将成功补全拼回批次。在DeepMath-103K上用DeepSeek-R1-Distill-Qwen-1.5B、n=5配对种子、1000步评估，LSPO在16个(基准,pass@k)组合中15胜1平，AIME24/pass@4提升+10.7点，MATH500/pass@1提升+2.4点，平均提升+3.8点。
LoRA Scaffolded Policy Optimization (LSPO): A Sampling-Time Low-Rank Scaffold for Recovering Reinforcement-Learning Gradient on Zero-Reward Cliff Prompts
Reinforcement learning from verifiable rewards (RLVR) for mathematical reasoning suffers from a structural blind spot: on "cliff" prompts-those on which every sampled rollout in a group fails-the group-normalized advantage is identically zero, so GRPO produces no gradient on precisely the prompts at the frontier of the model's capability. We introduce LoRA Scaffolded Policy Optimization (LSPO), a sampling-time mechanism that recovers this lost gradient. Each RL step, LSPO detects cliff prompts, fits a small low-rank (LoRA) adapter by a brief supervised step on their ground-truth solutions, re-rolls the cliffs with the base-plus-adapter model, splices the now-successful completions back into the RL batch with an importance-sampling correction, and takes a GRPO step on the base alone; the adapter receives only the supervised gradient and is discarded at checkpoint, yielding a base-only model. On DeepMath-103K with DeepSeek-R1-Distill-Qwen-1.5B, evaluated over n=5 paired seeds per arm at a matched 1000-step reporting horizon, LSPO's 5-seed mean matches or beats a DAPO baseline on all 16 (benchmark, pass@k) cells (15 strict wins and one exact tie), with gains of up to +10.7 points on AIME24/pass@4, +6.7 points on AIME24 and AIME26 at pass@16, and +2.4 points on MATH500/pass@1; averaged over the 16 cells the improvement is +3.8 points.