Function-Space Temporal Self-Distillation for Policy Optimization

Reinforcement learning with verifiable rewards (RLVR) has become a standard paradigm for improving large language models (LLMs) on various tasks, yet its sparse outcome rewards lack token-level credit assignment for intermediate steps. To address this, on-policy self-distillation (OPSD) leverages a self-teacher with privileged context to provide additional dense learning signals. However, because the self-teacher is often overconfident and imposes excessive penalties on long reasoning trajectories, OPSD frequently struggles in practice. To mitigate this, we propose self-instructing policy optimization (SIPO) with a contrastive self-teacher to provide dense credit. At each iteration, SIPO samples multiple rollouts per prompt from the current policy, scores them with environment rewards, and constructs two teacher contexts for each rollout by pairing the reference answer with mistakes made within the group. The model then re-evaluates its own responses under both contexts, using the difference between the two teacher log-probabilities as token-level feedback, so that biases shared by both contexts are expected to largely cancel. The resulting objective yields a token-level advantage for every rollout: the reward still sets the main direction of each update while the self-teacher redistributes credit across tokens. Even in groups where every rollout fails and group-relative advantages vanish, SIPO still provides a learning signal. By preserving direct optimization of the task reward while providing dense, token-level feedback, this approach bridges reinforcement learning and on-policy self-distillation. Extensive experiments across multiple reasoning and code-generation benchmarks demonstrate that SIPO outperforms both RLVR and OPSD baselines without an external teacher or additional generation.

Reinforcement learning with verifiable rewards (RLVR) enables large language models (LLMs) to continuously self-improve their reasoning capabilities. Compared to RLVR's scalar rewards, recent self-supervised on-policy distillation methods leverage denser supervision signals. However, both paradigms suffer from exploration bottlenecks, struggling to escape local optima when the policy fails to sample valid solutions. Relying on external demonstrations can bypass this issue; however, the off-policy nature hinders genuine self-improvement and the mismatched-distribution reasoning can not be fully exploited. In this work, we propose Self-Evolution Policy Optimization (SEPO), a framework that drives continuous reasoning capability evolution via guided exploration and in-distribution exploitation. Specifically, SEPO utilizes labels to elicit correct reasoning from the policy, unlocking the exploration potential. By treating current policy conditioned on this in-distribution reasoning as a self-teacher, SEPO distills the newly discovered solution back into the policy. Through this iterative cycle of policy-intrinsic exploration and exploitation, SEPO achieves robust and continuous capability evolution. Across scientific, tool-use, and complex logical reasoning domains, SEPO consistently achieves the best performance under identical training time or steps, demonstrating superior efficiency and convergence ceilings. Notably, SEPO maintains stable improvements even in scenarios where baselines severely underperform or fail entirely, such as on complex tasks or with small-scale models. Our code is available at https://github.com/Eric8932/SEPO.

Reinforcement learning with verifiable rewards (RLVR) improves the reasoning capabilities of large language models using automatically verifiable outcome signals, but these signals are typically sparse and at the sequence-level. On-policy self-distillation (OPSD) mitigates this sparsity by querying a privileged teacher at student-visited prefixes and providing dense token-level distributional supervision. Although this dense supervision alleviates signal sparsity, we find that standard OPSD still underexploits the temporal structure of the rollout. It assigns every local divergence the same coefficient, regardless of its position or the divergence sequence in which it occurs. In on-policy autoregressive generation, the same divergence magnitude can follow different discrepancy histories, reflecting different evolutions of the mismatch between the teacher and student. Since the local scalar alone cannot distinguish these temporal contexts, standard OPSD cannot adapt its token-level weights to the realized discrepancy sequence. To address this limitation, we propose Divergence-Adaptive Supervision Horizons (DASH). DASH maps the gap between each local distillation signal and the sequence-level mean to an adaptive propagation gate and then uses these gates to control backward multi-step aggregation. By doing so, DASH adjusts token-level supervision weights according to how local divergences evolve during generation. Experiments on three mathematical reasoning benchmarks across three model scales show that DASH improves over our matched vanilla OPSD reruns on every benchmark at all three scales. DASH reuses the teacher and student distributions that OPSD already computes, so the gains require no additional teacher or student forward pass. Code: https://github.com/DBtxy/DASH-OPSD