Trust Is Not Enough: Influence Calibration for On-Policy Self-Distillation in Agentic RL

Large language model agents are commonly trained through reinforcement learning with sparse trajectory-level rewards, which offer limited guidance on how strongly individual tokens should be updated. On-Policy Self-Distillation (OPSD) addresses this by re-scoring generated tokens under a privileged replay view to obtain dense, token-level supervision. However, we identify a confounding issue: the resulting support may reflect both the privileged information contained in the replay view and score shifts induced by the replay scaffold, making it difficult to attribute the support specifically to that information. This issue is especially pronounced when future environment observations serve as privileged information, since replaying them requires reconstructing an extended scaffold that itself perturbs token scores. To resolve this confounding, we propose Observation-Calibrated Self-Distillation (OCSD), which contrasts two structurally matched replay views, Full and Observation-Ablated, differing only in whether the actual future observation is present, to derive an observation residual that discounts score changes shared by the replay scaffold. OCSD then applies this residual to modulate token-level GRPO updates at high-uncertainty steps, while preserving the trajectory-level update direction. Experiments on ALFWorld, WebShop, and Search-QA across three Qwen3 model scales show that OCSD consistently outperforms strong baselines. Diagnostic analyses further confirm that the calibrated residual aligns better with local environment feedback. Our code is publicly available at https://github.com/yiy1x/OCSD.

Large language model agents have shown strong potential in complex interactive tasks, yet their reinforcement learning (RL) is often hindered by sparse rewards, as a long multi-turn trajectory may receive only a single outcome-level signal. On-policy self-distillation (OPSD) provides dense token-level supervision from a privileged teacher, but the teacher may not be reliable at every position. Existing methods commonly rely on isolated token-level discrepancies, which can be sensitive to noise, or assign a shared step-level weight that may overlook positional variation. We propose Persistent Consistency Self-Distillation (PCSD), which derives token-level distillation weights from the local persistence of teacher-favoring signals. PCSD combines adaptive windows with exponentially decayed aggregation to capture persistent relative teacher support, applies trend-aware modulation to attenuate locally declining support, and produces continuous weights through sigmoid gating. The resulting objective is jointly optimized with GRPO, combining dense teacher guidance with sparse environmental feedback. Without inference-time skills, PCSD achieves the best ALFWorld Overall results among all baselines on both backbones, exceeding GRPO by 15.6 and 13.3 points and SDAR by 6.2 and 5.5 points, while remaining competitive on WebShop and gaining 15.8 points over GRPO on unseen ALFWorld split.

On-policy self-distillation (OPSD) improves the reasoning abilities of LLMs by internalizing privileged context into model parameters through self-distillation. Two recent research lines promote vanilla OPSD by choosing which tokens to learn from and by controlling how much privileged information the teacher receives, respectively. However, we show that each line optimizes one variable while holding the other fixed, which leads to a suboptimal solution. We argue that the two variables are coupled through the student's learning capacity: the privileged information sets the per-token divergence the teacher prescribes, while token weighting selects which of these the student must absorb. We formalize the two lines of work into a unified optimization framework, which maximizes the aggregate teacher--student divergence, subject to a budget on the aggregate learning difficulty the student can absorb. Under this modelling, we propose Unified On-Policy Self-Distillation (USD), a lightweight online algorithm to solve the Lagrangian. USD reveals that a single dual variable governs both decisions: at one price for learning difficulty, it simultaneously sets the token-selection threshold and the direction of privileged-information adjustment, keeping supervision matched to the student's evolving capacity. Through extensive experiments, USD consistently demonstrates superior performance over OPSD and token- and PI-side baselines across various model scales on various reasoning benchmarks. Code is available at https://github.com/lauvlalala/USD.