Group Relative Policy Optimization (GRPO) has become a standard approach for improving the reasoning abilities of large language models, but its training is costly because each step requires generating many long reasoning responses. Recent methods use speculative decoding to accelerate the rollouts, where a draft model proposes tokens that the target model verifies. However, we find that the draft model repeatedly misses the same tokens within a response and across responses in the same GRPO group, and the verification feedback on these misses is not used to update the draft during the rollout. Motivated by this analysis, we introduce SPARK, a lightweight self-adaptive mechanism designed to enhance draft models used in speculative GRPO training. SPARK leverages target verification feedback to refine draft predictions during generation while preserving their existing training procedures. Averaged across 21 model-dataset settings, SPARK improves generation speedup by 32.7% and 11.4%, and end-to-end GRPO training speedup by 32.2% and 8.5%, over EAGLE3-style and DFlash-style baselines, respectively.

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