SimpleOPD: Simple Tokenizer-Agnostic On-Policy Distillation for Long-Context Reasoning

On-policy distillation (OPD) leverages dense teacher rewards to enhance reasoning models. However, scaling OPD to long-horizon tasks exposes a critical flaw: as the student's generated prefix inevitably diverges from the teacher's thought process, the teacher's dense reward loses local exploitability. Continuing to generate and evaluate tokens on these ``drifted'' trajectories not only degrades reward quality but also incurs massive computational waste. To address this, we introduce Prune-OPD, a framework that dynamically aligns training budgets with supervision quality. By continuously monitoring the local compatibility between student and teacher predictions (e.g., via top-$k$ overlap), Prune-OPD detects prefix-drift events in real time. Upon detecting severe drift, it monotonically down-weights subsequent unreliable rewards and triggers dynamic rollout truncation. This allows the training process to halt futile generation and reallocate compute strictly to reliable teacher supervision. Across diverse teacher-student combinations, Prune-OPD consistently aligns computation with supervision reliability. When prefix drift makes dense teacher rewards unreliable, it reduces training time by 37.6%--68.0% while preserving, and often improving, performance on challenging benchmarks (AMC, AIME, HMMT). When student-teacher compatibility remains high, it automatically preserves long-context supervision by expanding the training window. These results suggest that Prune-OPD improves OPD not by blindly shortening rollouts, but by reallocating computation toward locally exploitable teacher rewards.

On-policy distillation (OPD) improves the reasoning capabilities of small language models through token-level teacher supervision on student-generated trajectories. Yet can teachers that excel at solving problems independently also guide student reasoning effectively? Prior work shows that when student prefixes follow reasoning paths that differ from the teacher's own or contain errors, teachers can be less accurate when continuing from these prefixes than when solving problems independently. To this end, we propose Prep-OPD, which uses reinforcement learning (RL) before distillation to train the teacher to adapt to the student's existing reasoning state and correct course when errors arise. Training optimizes teacher continuations from fixed student prefixes using final-answer correctness as the reward. The prepared teacher then trains the student through trajectory guidance and token-level supervision. We evaluate Prep-OPD on eight mathematical reasoning benchmarks, using Qwen3-4B-Instruct-2507 as the teacher and Qwen3-0.6B and Qwen3-1.7B as students. With the 4B teacher and 1.7B student, Prep-OPD improves average accuracy over standard OPD and the strongest baseline, Relay-OPD, by 8.28 and 2.30 percentage points, respectively. Controlled experiments further show that teacher RL conditioned on student-generated prefixes yields higher student accuracy than problem-start teacher RL with and without handoff on Qwen3-1.7B. Reusing the same prepared teacher also improves Qwen3-0.6B.

On-policy distillation (OPD) combines student-generated rollouts with dense token-level supervision from a teacher, but providing such supervision for every rollout requires substantial teacher computation. We introduce Success-Referenced On-Policy Distillation (SR-OPD), which reduces this cost by selecting which prompts and rollouts receive teacher supervision. When the student produces both successful and failed rollouts for the same prompt, a successful rollout can serve as a natural reference for selecting failed rollouts. SR-OPD therefore focuses on such prompts and prioritizes failed rollouts whose hidden-state trajectories show sustained divergence from a successful reference, while accounting for estimated teacher-input cost. Across three teacher-student pairs and six mathematical reasoning benchmarks, SR-OPD uses only 3.46-5.02% of the teacher-input tokens required by Vanilla OPD in the one-pass setting while maintaining comparable reasoning performance. Under a controlled setting matched to 5% of Vanilla OPD's teacher-input budget, further experiments support both key design choices: focusing supervision on prompts with both successful and failed rollouts, and using successful rollouts to guide failure selection. These results indicate that a student's own successful behavior can serve as a useful reference for allocating teacher supervision under a fixed teacher-input budget.