PIVOT: Progressive Intervention via Online Teacher Correction

Reinforcement learning with verifiable rewards (RLVR) and on-policy distillation (OPD) have become two main paradigms for post-training reasoning models. RLVR gives each response a single outcome label, leaving the steps inside it without separate credit. OPD provides token-level guidance at student-visited prefixes, but its pointwise signal does not directly reflect the pattern of teacher--student disagreement across the vocabulary. Dense, unbounded log-ratio supervision can amplify the teacher's influence, yet a strong solver is not necessarily a suitable guide when the student's solution paths depart from the teacher's. We propose Residual Advantage (\RA{}), which treats the teacher--student probability residual as a bounded one-step reward, subtracts the corresponding state value under the student policy to form a standard advantage, and centers the result within each response before adding it to the verifier advantage. The guidance term has zero mean within each response, so the verifier advantage remains the response's mean label and the teacher only redistributes credit among the steps within it. \CoRA{} further updates a teacher LoRA with verifier advantages on the same scored student batch and uses the updated teacher in the next iteration's residual, adapting guidance to the student's attempts. With Qwen3-1.7B-Base and Qwen3-4B-Base students and a Qwen3-8B teacher, \RA{} combined with GRPO or REINFORCE++ improves the underlying sequence-advantage algorithm in all 24 comparisons on three mathematical benchmarks, raising macro Avg@8 by 1.7--3.6 points and Pass@8 by 3.9--6.3 points. Both combinations surpass teacher-only OPD, and \CoRA{} adds a further 1.0--1.5 Avg@8 points.

Reinforcement learning with verifiable rewards (RLVR) via Group-Relative Policy Optimization (GRPO) is widely used for multi-turn VLM agent training, yet it suffers from zero-gradient silence on uniform failures and coarse episode-level credit assignment. While On-Policy Distillation (OPD) and On-Policy Self-Distillation (OPSD) mitigate sparse rewards using hindsight information, their underlying mechanisms remain poorly understood. Through controlled counterfactual rollback probes across five multi-turn VLM agent benchmarks, we reveal that performance gains in OPSD/OPD are largely driven by physical state rollback at the pivot step, defined as the first unrecoverable action without remaining step budget. However, physical state rollbacks are computationally prohibitive and infeasible in real-world environments. To bridge this gap, we present Pivot-Aware Internalized Visual On-Policy Training (PIVOT), an RL framework that internalizes pivot localization and state restoration directly into token-level parameter updates, eliminating environment rollbacks during RL training and additional skill hints at test time. PIVOT unifies three functional roles within a single architecture: a failure Analyzer non-invasively localizes the pivot step and diagnoses failure modes from visual trajectory collages and action logs; a detached Teacher re-scores failed tokens under this privileged diagnostic context; and a Student optimizes joint GRPO and confidence-gated OPD objectives. At test time, both Teacher and Analyzer branches are stripped. Evaluated on five multi-turn VLM agent tasks across cognitive grid puzzles, 3D embodied control and navigation, and generative reasoning, PIVOT achieves 0.90 overall accuracy on Qwen2.5-VL-3B (+8% over SFT+GRPO baseline and +5% over previous SOTA) and scales to 0.92 on Qwen3-VL-2B (+12% over SFT+GRPO baseline).

Reinforcement Learning from Verifiable Rewards (RLVR) is a key driver for Large Reasoning Models, but it is vulnerable to "zero-reward collapse", a training failure where a sudden increase in task difficulty causes the learning signal to vanish. We argue that the conventional approach of discarding these failed trajectories is wasteful, as they contain valuable diagnostic information about the model's cognitive gaps, a bright side that can be leveraged for recovery. Existing solutions, however, often regress to static, "off-policy-style" interventions like pre-defined hint libraries or perform post-hoc refinement, failing to provide the adaptive, forward-looking guidance needed to escape the collapse. To address this, we propose a paradigm shift towards on-policy pedagogical intervention and introduce MENTOR, a multi-agent framework that acts as a live mentor. MENTOR diagnoses the root cause of failure in real-time and dynamically generates targeted, instructional prompts to guide the learning agent's next attempt. As a plug-and-play module, MENTOR integrates seamlessly into existing policy optimization pipelines like GRPO without modifying the training infrastructure. Extensive experiments on math and code generation show that MENTOR effectively mitigates zero-reward collapse, outperforming state-of-the-art baselines. Notably, it achieves massive average relative gains of up to 78.3% on Llama-3.2-3B-Instruct over its base model.