We study on-policy distillation (OPD) for agentic tasks, where an LLM agent interacts with an environment over multiple turns and a student imitates a teacher over these multi-turn interaction histories. Fully online OPD is costly because each update requires fresh student rollouts through the environment and teacher queries at visited histories. We propose Replayed-Prefix On-Policy Distillation (ReOPD), an off-environment alternative that reuses pre-collected teacher trajectories as replayed prefixes: the student acts at selected steps, while the teacher provides dense per-step supervision without executing new environment interactions. We show that multi-turn OPD introduces a prefix trap: making histories more student-on-policy improves relevance to the student, but can query the teacher on histories where its target is unreliable. This creates a two-sided distribution shift between student occupancy and teacher reliability. ReOPD addresses this by treating multi-turn OPD as a reliability-aware prefix distribution design and implements it with a simple step-decaying sampling schedule that emphasizes early, lower-shift prefixes. Across mathematical reasoning with Python and search environments over multiple teacher and student model scales, ReOPD preserves or improves OPD-level accuracy, uses zero tool calls during student training, and is at least 4$\times$ faster per rollout than OPD. ReOPD therefore turns expensive agent-environment interaction into a reusable offline resource, enabling scalable distillation across tools, tasks, and environments.
Baohao Liao, Hanze Dong, C. Monz et al.· 7 citations· ⚡1
Two forms of test-time scaling for Large Language Models (LLMs) have emerged as effective and widely adopted paradigms: sequential, in which later answer attempts depend on earlier ones, and parallel, such as i.i.d. sampling with reranking. In this study, we investigate their properties in translation. First, our study shows that sequential sampling has a higher performance ceiling, providing a more diverse and effective pool of samples, particularly under smaller sampling budgets. Second, we interrogate the nature of test-time scaling through a multidimensional manual analysis. Human analysis of the Best-of-N translations demonstrates that sequential sampling substantially improves translation fluency and naturalness, but can degrade accuracy when inference budgets are large. Finally, we suggest an explanation of the mechanism through which sequential scaling improves machine translation. Our controlled analysis partially attributes the success of sequential self-improvement to the model's access to a larger target-side context. Ablation experiments on sequential sampling demonstrate its robustness across different sampling temperatures, while also revealing sensitivity to context construction, suggesting directions for future improvement.