Expected Reasoning-Step Return Unifies On-Policy Learning from Rewards and Teachers
cs.AI
Submitted: 2026-09-26
Updated: 2026-09-26
Comments: 32 pages, 10 figures
License: http://creativecommons.org/licenses/by/4.0/
The gist: On-policy reasoning models can learn from task rewards or teacher signals, but these sources differ in form and can favor conflicting updates, leaving unclear which should guide a given reasoning
Terminology
Abstract
On-policy reasoning models can learn from task rewards or teacher signals, but these sources differ in form and can favor conflicting updates, leaving unclear which should guide a given reasoning action. We introduce Expected Reasoning-Step Return (ERSR), which treats semantic reasoning steps as macro-actions and uses Monte Carlo student-policy rollouts to estimate the expected final task reward of student-generated and teacher-proposed actions in a common return space for step-level comparison. ERSR analysis reveals an outcome-dependent asymmetry: student actions are more beneficial than teacher replacements on successful trajectories, whereas teacher replacements become more beneficial on failed trajectories. We further show that student answer-probe gains track student-step ERSR utility and distinguish beneficial from harmful reasoning steps. Based on these findings, we propose Return-Referenced On-Policy Learning (R squared OPL), which reinforces student reasoning on successful trajectories and distills teacher signals on failed ones, while using group success rate for difficulty scaling and student-probe gains for step-level modulation. Experiments across reasoning benchmarks and teacher--student configurations show that R squared OPL consistently outperforms strong baselines. ERSR training dynamics further show that R squared OPL jointly exploits substantial utility from both reward- and teacher-side signals, whereas existing hybrids often leave substantial residual utility in one branch.
Sources
- Reward-Gated On-Policy Distillation
- MiniMax-M1: Scaling Test-Time Compute Efficiently with Lightning Attention
- SEED-GRPO: Semantic Entropy Enhanced GRPO for Uncertainty-Aware Policy Optimization
- Does On-Policy Distillation Really Distill? From Noisy Teacher to Self-Improvement
- Rethinking On-Policy Distillation of Large Language Models II: One Training Example
- Soft Adaptive Policy Optimization
- Gemma 4 Technical Report
- DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning
- On-Policy RL with Optimal Reward Baseline
- On-Policy Delta Distillation
- Distilling the Knowledge in a Neural Network
- REINFORCE++: Stabilizing Critic-Free Policy Optimization with Global Advantage Normalization
- Reinforcement Learning via Self-Distillation
- Bridging Reasoning Trajectories in On-Policy Distillation via Near-Future Guidance
- Entropy-Aware On-Policy Distillation of Language Models
- VinePPO: Refining Credit Assignment in RL Training of LLMs
- DistiLLM: Towards Streamlined Distillation for Large Language Models
- Scaling Reasoning Efficiently via Relaxed On-Policy Distillation
- Sequential Beats Joint: On the Interplay between On-Policy Distillation and RLVR
- Unifying Group-Relative and Self-Distillation Policy Optimization via Sample Routing
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