Beyond Trajectory Imitation: Strategy-Guided Policy Optimization for LLM Reasoning
Authors: Tianyuan Shi, Canbin Huang, Bei Li, Xin Chen, Xiaojun Quan, Jingang Wang, Qifan Wang
Organizations: School of Computer Science and Engineering, Sun Yat-sen University, China · Meituan, Inc., China · Shenzhen Loop Area Institute, China · Meta AI, USA
Abstract
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.
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.
On-policy self-distillation (SD) improves LLM reasoning by using teacher-side privileged information (PI) to turn sparse verifier outcomes into dense token-level supervision. Existing methods usually assume trusted PI, such as reference answers or successful traces. We ask whether PI can instead come from an experience-derived skill bank, where retrieved skills are compact and reusable but may also be irrelevant or misleading. We propose Skill-Conditioned Gated Self-Distillation (SGSD), which formulates skill-based SD as teacher hypothesis validation rather than unconditional imitation. SGSD retrieves skill-mistake pairs, constructs a multi-teacher pool, and lets all skill-conditioned teachers score the same plain-prompt student rollout. The verifier validates each teacher's polarity: supporting a success or suppressing a failure gives positive supervision, while the opposite stance is reversed. A robust gated objective then distills informative teacher-student disagreements while suppressing uncertain or extreme signals. Experiments on multiple mathematical reasoning benchmarks show that SGSD consistently improves over GRPO and remains competitive with answer-conditioned OPSD under a weaker PI assumption. For example, on Qwen3-1.7B, SGSD outperforms GRPO by 6.2% and OPSD by 1.7% on average on AIME24, AIME25, and HMMT25.
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.