Recent Large Reasoning Models (LRMs) achieve strong performance by leveraging long-form Chain-of-Thought (CoT) reasoning, but uniformly applying overlong reasoning at inference time incurs substantial and often unnecessary computational cost. To address this, prior work explores various strategies to infer an appropriate reasoning budget from the input. However, such approaches are unreliable in the worst case, as estimating the minimal required reasoning effort is fundamentally difficult, and they implicitly fix the trade-off between reasoning cost and accuracy during training, limiting flexibility under varying deployment scenarios. Motivated by these limitations, we propose ORBIT, a controllable multi-budget reasoning framework with well-separated reasoning modes triggered by input. ORBIT employs multi-stage reinforcement learning to discover Pareto-optimal reasoning behaviors at each effort, followed by on-policy distillation to fuse these behaviors into a single unified model. Experiments show that ORBIT achieves (1) controllable reasoning behavior over multiple modes, (2) competitive reasoning density within each mode, and (3) integration of these frontier policies into a single unified student model while preserving clear mode separation and high per-mode performance.

Existing Reinforcement Learning from Verifiable Rewards (RLVR) methods, such as Group Relative Policy Optimization (GRPO), have achieved remarkable progress in improving the reasoning capabilities of Large Reasoning Models (LRMs). However, they exhibit limited exploration due to reliance on on-policy rollouts which are confined to the current policy’s distribution, resulting in narrow trajectory diversity. Recent approaches attempt to expand policy coverage by incorporating trajectories generated from stronger expert models, yet this reliance increases computational cost and such advanced models are often inaccessible. To address these issues, we propose In-Context Steered Policy Optimization (ICPO), a unified framework that leverages the inherent in-context learning capability of LRMs to provide expert guidance using existing datasets. ICPO introduces mixed-policy GRPO with implicit expert forcing, which expands exploration beyond the current policy distribution without requiring advanced LRM trajectories. To further stabilize optimization, ICPO integrates expert region reject sampling to filter unreliable off-policy trajectories and annealed expert-bonus reward shaping to balance early expert guidance with later autonomous improvement. Results demonstrate that ICPO consistently enhances RLVR performance and training stability on mathematical reasoning benchmarks, revealing a scalable and effective RLVR paradigm for LRMs. Our code is available at https://github.com/Celine-hxy/ICPO.

On-policy distillation (OPD) transfers reasoning behavior by training a student on teacher feedback along student-generated trajectories, but standard full-rollout training ties every update to a costly completion and can over-allocate supervision to late positions with low marginal value for the current student. We revisit this assumption through the useful supervision horizon: student-induced rollouts can drift from teacher-preferred continuations, while aligned prefixes may already preserve the long-horizon OPD update direction. We propose ADWIN, an adaptive-window framework for OPD that treats rollout length as an online admissibility decision, training on short teacher-anchored prefixes while using delayed full-rollout probes to audit prefix–full alignment and adapt the next horizon with staleness control. Across math and code reasoning benchmarks in single-task, multi-task, and strong-to-weak settings, ADWIN improves the accuracy–compute trade-off over full-rollout OPD and prefix-based baselines, reducing end-to-end training cost by up to 4.1× while achieving comparable or better accuracy.

Reinforcement learning with verifiable rewards (RLVR) has significantly boosted the reasoning capability of language models (LMs). However, existing RLVR approaches train LMs based on their own on-policy responses and are constrained by the initial capability of LMs, thus prone to exploration stagnation, in which LMs fail to solve more training problems and cannot further learn from the training data. Some approaches try to address this by leveraging off-policy solutions to training problems, but rely on external expert guidance that is limited in availability and scalability. In this work, we propose LTE (Learning to reason from Trial and Error), an approach that hints LMs with their previously self-made mistakes, not requiring any external expert guidance. Experiments validate the effectiveness of LTE, which outperforms the normal group relative policy optimization (GRPO) by 5.02 in Pass@1 and 9.96 in Pass@k on average across six mathematical reasoning benchmarks for Qwen3-8B-Base and even performs better than methods that require external guidance. Further analysis confirms that LTE successfully mitigates exploration stagnation and enhances both exploitation and exploration during training. Our code is available at https://github.com/JamyDon/LTE.