Prefix-Guided On-Policy Distillation: Mining Golden Trajectories from Rollouts

On-policy distillation (OPD) improves reasoning models by applying dense teacher supervision on student-sampled trajectories. However, scaling OPD to long-horizon mathematical reasoning exposes a reliability and efficiency problem: standard OPD assigns every sampled candidate the same long rollout budget, even though some trajectories may quickly become weakly aligned with the teacher and provide less useful supervision. Prior analyses suggest that successful OPD depends on local teacher-student compatibility, which can be measured by top-k overlap on student-visited prefixes. When this overlap is low, continuing to generate or train on long suffixes may waste computation and introduce noisy learning signal. To address this, we introduce Prefix-Guided On-Policy Distillation (PG-OPD), a simple rollout-allocation framework that uses fixed-length prefixes to estimate trajectory value before expensive long-horizon generation. PG-OPD first decodes every sampled candidate to the same prefix length, computes teacher-student top-k overlap within an early probe window of that prefix, and selectively continues high-overlap candidates to a fixed long length. Low-overlap candidates stop at the fixed prefix, avoiding unnecessary suffix generation. Across diverse teacher-student combinations on AMC, AIME, and HMMT benchmarks, PG-OPD improves average accuracy by up to 4.80 points while reducing training time by up to 2.46x. These results suggest that prefix-level compatibility provides a practical signal for directing OPD computation toward trajectories that remain learnable from the teacher.