Know When to Stop, Where to Restart: Accelerating Multi-Turn Agentic On-Policy Distillation

Abstract:On-policy distillation (OPD) has become a standard approach for transferring capabilities from large teachers to compact students. Its cost, however, is dominated by autoregressive student rollouts and scales poorly in multi-turn agentic settings. Existing acceleration methods truncate or relocate the supervision signal according to fixed, offline budgets, despite substantial variation in teacher-signal reliability both within and across trajectories. Our empirical analysis on $\tau^2$-bench reveals a clear structure in this variation: informative supervision is concentrated in the prefix of each turn, and, most importantly for multi-turn agentic training, the cross-turn loss of teacher endorsement is temporally locked to the student's first erroneous action rather than accumulating gradually over turns. Building on these findings, we propose STRIDE (Stop-and-Restart on-policy Distillation acceleration), which combines two complementary techniques: adaptive early stopping, which terminates a rollout once the cumulative teacher log-probability falls below an out-of-distribution threshold, and a prefix buffer, which caches high-quality prefixes and restarts generation at the weakest correct turn. Together, these mechanisms induce a data-driven curriculum that progressively extends coverage to later turns. On $\tau^2$-bench retail, our method matches full-trajectory OPD and exceeds the 30B teacher at a $3.73\times$ speedup, surpasses the baseline itself at $2.34\times$, and retains a $4.51\times$ speedup under cross-domain multi-teacher training. As a supplementary generalization test beyond the agentic setting, STRIDE outperforms full OPD on AIME 2025 at a $5.10\times$ speedup and on AIME 2024 at a $3.08\times$ speedup; averaged across the two evaluations, both fixed-budget truncation baselines remain below full OPD.

Machine Learning (cs.LG); Computation and Language (cs.CL)

arXiv:2609.14636 [cs.LG]

(or arXiv:2609.14636v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.14636 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.