Matching Supervision to the Student's Learning Capacity: A Unified Framework for On-Policy Self-Distillation

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.

Meta-Cognitive Memory Policy Optimization for Long-Horizon LLM Agents

Memory-augmented LLM agents tackle complex long-horizon tasks by recursively summarizing interaction trajectories into compact memory. However, existing approaches typically train these memory policies using outcome-based reinforcement learning, failing to localize where intermediate memory quality degrades. As interactions unfold, ambiguous recursive summaries progressively discard task-relevant information and introduce semantic noise. This exacerbates belief deviation, obscuring the agent's estimate of the latent task state and ultimately derailing long-horizon reasoning. We therefore argue that memory optimization should focus not merely on trajectory-level success, but on the clarity of the belief induced by intermediate summaries. To this end, we introduce Belief Entropy, a self-supervised proxy that probes how uncertain the model remains about the latent task state given its current memory. Based on this proxy, we propose Metacognitive Memory Policy Optimization (MMPO). Instead of relying only on sparse outcome-based signals, MMPO provides fine-grained, memory-specific supervision via explicitly penalizing summaries that induce high epistemic uncertainty. Experiments show that MMPO consistently outperforms existing methods on diverse long-horizon tasks, maintaining 97.1% performance even when scaled to 1.75M-token contexts.