SocraticPO: Policy Optimization via Interactive Guidance
Authors: Zirui Liu, Jie Ouyang, Qi Liu, Xianquan Wang, Jiayu Liu, Tingyue Pan, Qingchuan Li, Jing Sha, +3 more
Organizations: State Key Laboratory of Cognitive Intelligence, University of Science and Technology of China · iFLYTEK AI Research (Central China), iFLYTEK Co., Ltd
Abstract
Reinforcement learning (RL) for large language models usually supervises reasoning with scalar outcome rewards, such as binary correctness. Such rewards provide an optimization direction but rarely explain how a model should revise its mistaken reasoning, which can encourage shortcut learning and brittle policies. We propose \textbf{SocraticPO} (Socratic Policy Optimization), a policy-optimization framework that augments RL rollouts with Socratic-style natural-language guidance. During rollout, the student first answers independently; if the answer is incorrect, a teacher diagnoses the attempt and provides concise corrective guidance, after which the student continues under the expanded context. Crucially, this guidance is paired with reward decay: correct answers obtained after teacher intervention only receive decayed rewards, preventing the policy from treating teacher help as a free path to reward. Since SocraticPO only modifies the rollout process while leaving the standard expected-reward objective intact, it can be plugged into existing policy-gradient backends such as Reinforce++. Moreover, because the teacher provides only text-level guidance, SocraticPO can leverage stronger black-box teacher models without requiring access to logits or distribution matching. On undergraduate-level scientific reasoning benchmarks from SciKnowEval, SocraticPO improves over strong RL and self-distillation baselines. Ablations show that both targeted guidance and reward decay are necessary, with reward decay mitigating reliance on assisted correction.
GRPO-style RLVR trains reasoning models from multiple on-policy attempts per prompt, but typically uses these attempts only through terminal rewards. We show that a mixed group contains a richer process signal: a correct completion is a self-generated witness of how the current policy can solve the problem, while a wrong completion provides on-policy prefixes where the policy needs correction. We introduce \emph{Self-Supervised On-Policy Distillation} (SSOPD), which distills a teacher distribution conditioned on the shortest correct completion into prefixes of the longest wrong completion. This converts intra-group correct--wrong contrast into dense process supervision without external solution traces. A stopping-time view motivates the shortest-correct / longest-wrong rule as a finite-group approximation to editing persistent failures toward fast-success actions, and a prompt-level frontier weight concentrates the auxiliary loss where correct and wrong branches coexist. Across AIME 2024, AIME 2025, and HMMT 2025, SSOPD improves over GRPO in all nine model-benchmark settings. On Qwen3-8B, it reaches a macro Avg@12 of 65.6, outperforming GRPO by 1.6 points and the solution-conditioned OPSD baseline by 0.8 points. Code will be released at https://github.com/tzq1999/SSOPD.
Existing reinforcement learning methods for LLM reasoning implicitly assume that the policy generating training trajectories should coincide with the one producing inference responses. We argue that this is a misleading inductive bias: the optimization-optimal trajectory distribution favors informative gradients, whereas the inference-optimal response distribution emphasizes accuracy and consistency. Forcing both into a single policy entangles their gradients and suppresses exploration. We propose R2PO (Residual Rollout Policy Optimization), which attaches a lightweight Residual Rollout-Head atop the policy to decouple training trajectories from inference responses, diversifying rollouts during training while keeping inference generation intact. Experiments show that R2PO consistently outperforms baselines, with average accuracy gains of 3.4% on MATH-500 and 1.3% on APPS, alongside more diverse rollouts and reduced length bias. Our code is available at https://github.com/RRPO-ARR/Code.
Distilling reasoning capabilities from strong to weak language models typically involves imitating specific solution trajectories, effectively transferring what to answer rather than how to reason. This trajectory-level imitation encourages memorization of instance-specific steps rather than acquisition of transferable problem-solving skills, limiting generalization to novel problems. We propose Strategy-Guided Policy Optimization (SGPO), which replaces instance-level trajectory imitation with reusable strategy distillation. SGPO extracts structured strategy descriptions from strong-model responses and, for each problem, constructs both autonomous and strategy-guided trajectories to enable direct comparison of the model's behavior with and without strategic guidance. The framework then addresses two key questions. For how to distill, a token-level forward-KL objective selectively transfers the distributional shift induced by strategy conditioning into the unguided policy, with proximal constraints ensuring stability. For when to distill, adaptive instance-level weighting strengthens guidance when autonomous exploration falls short and reduces it as the model's own competence grows. Experiments on four mathematical benchmarks across two model families show that SGPO consistently outperforms SFT, on-policy RL, and hybrid-policy baselines, improving the average score by 2.2 points over the strongest baseline on Qwen2.5-7B-Instruct. Analysis reveals that the forward-KL objective provides an inherently selective distillation signal that outperforms direct trajectory imitation, and that strategy distillation exhibits complementary scaling with base model capability.