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arxiv: 2606.24064 · v1 · pith:XPJIB7NKnew · submitted 2026-06-23 · 💻 cs.AI

Beyond Trajectory Imitation: Strategy-Guided Policy Optimization for LLM Reasoning

Tianyuan Shi , Canbin Huang , Bei Li , Xin Chen , Xiaojun Quan , Jingang Wang , Qifan Wang This is my paper

Pith reviewed 2026-06-26 00:37 UTC · model grok-4.3

classification 💻 cs.AI
keywords strategy distillationpolicy optimizationLLM reasoningforward KL divergencetrajectory imitationmathematical reasoningreinforcement learning
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The pith

SGPO replaces trajectory imitation with reusable strategy distillation via token-level forward-KL to improve LLM reasoning generalization.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes Strategy-Guided Policy Optimization to move beyond imitating specific solution paths in language models. Instead of transferring exact trajectories, it extracts structured strategy descriptions that can be reused across problems. By comparing model behavior with and without these strategies and using a selective forward-KL loss, the method transfers beneficial reasoning patterns. Experiments show consistent gains over standard fine-tuning and reinforcement learning approaches on mathematical benchmarks. This suggests that focusing on how to reason rather than what to answer improves generalization to new problems.

Core claim

Strategy-Guided Policy Optimization (SGPO) extracts structured strategy descriptions from strong-model responses and constructs both autonomous and strategy-guided trajectories for each problem. It applies a token-level forward-KL objective with proximal constraints to selectively transfer the distributional shift from strategy conditioning into the unguided policy, combined with adaptive instance-level weighting that adjusts guidance based on the model's autonomous performance. On four mathematical benchmarks across two model families, SGPO improves average scores by 2.2 points over the strongest baseline on Qwen2.5-7B-Instruct, with the forward-KL objective proving more effective than dire

What carries the argument

Token-level forward-KL objective that selectively distills the distributional shift induced by strategy conditioning into the unguided policy, with proximal constraints and adaptive instance weighting.

If this is right

  • SGPO outperforms SFT, on-policy RL, and hybrid-policy baselines by 2.2 points on average across math benchmarks.
  • The forward-KL objective supplies a more selective distillation signal than direct trajectory imitation.
  • Strategy distillation produces complementary performance gains as base model capability increases.
  • The framework applies successfully across two model families on four separate mathematical benchmarks.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the extracted strategies prove reusable in non-mathematical domains, the same distillation approach could transfer to coding or scientific reasoning tasks.
  • The selective property of forward-KL may reduce overfitting to specific training instances compared with full-trajectory imitation.
  • Adaptive weighting offers a route to training regimes in which external guidance is automatically phased out as the model improves.
  • The method implies that conditioning signals during optimization can transfer problem-solving skills more efficiently than final-answer supervision alone.

Load-bearing premise

Structured strategy descriptions extracted from strong-model responses remain sufficiently reusable and effective when transferred to new problems for weaker models.

What would settle it

Performance gains disappear on a held-out test set of problems whose underlying strategies differ markedly from those extracted in the training distribution.

Figures

Figures reproduced from arXiv: 2606.24064 by Bei Li, Canbin Huang, Jingang Wang, Qifan Wang, Tianyuan Shi, Xiaojun Quan, Xin Chen.

Figure 1
Figure 1. Figure 1: Overview of the SGPO framework. For each problem, we jointly construct an [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: KL direction. (a) The unguided policy covers multiple strategies; the guided distribu￾tion reflects one. (b) Reverse KL collapses onto the guided mode. (c) Forward KL absorbs the guided strategy while preserving alternatives. First, we adopt the forward KL direc￾tion (guided as reference). The strategy￾guided distribution concentrates on a par￾ticular strategy, whereas the unguided policy may cover multipl… view at source ↗
Figure 3
Figure 3. Figure 3: Training dynamics under ablation settings. (a)(b) Removing either autonomous [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Training dynamics of SGPO and SFT+GRPO. (a) Policy entropy: SGPO maintains [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Step-level KL analysis on a training example. Gray bars: direct SFT loss, declining [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: KL-based distillation yields faster convergence and a higher re￾ward ceiling than direct SFT on guided trajectories. The performance gap arises from the granularity of the learning signal. Direct SFT applies uniform fit￾ting pressure across all tokens, whereas the KL ob￾jective automatically concentrates optimization on tokens whose generation probability shifts most un￾der strategy conditioning [PITH_FUL… view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper proposes Strategy-Guided Policy Optimization (SGPO) to distill reasoning from strong to weak LLMs by extracting reusable structured strategy descriptions rather than imitating instance-specific trajectories. For each problem it constructs autonomous and strategy-guided trajectories, then applies a token-level forward-KL objective with proximal constraints to selectively transfer beneficial distributional shifts into the unguided policy, together with adaptive instance-level weighting that strengthens guidance when autonomous performance is weak. Experiments across four mathematical reasoning benchmarks and two model families report that SGPO outperforms SFT, on-policy RL, and hybrid-policy baselines, with a 2.2-point average gain over the strongest baseline on Qwen2.5-7B-Instruct; analysis attributes the gains to the selective nature of the forward-KL signal and complementary scaling with base-model capability.

Significance. If the central performance claim and its attribution to reusable strategy distillation hold after proper verification, the work would be significant for LLM reasoning research. It directly targets the memorization-vs-generalization limitation of trajectory imitation and introduces a concrete mechanism (token-level forward-KL plus proximal constraints) for selective transfer. The reported complementary scaling with model size is a useful empirical observation. The absence of quantitative checks on strategy reuse and divergence control, however, prevents the result from being treated as a settled advance at present.

major comments (3)
  1. [Abstract / experimental results] Abstract and experimental results section: the reported 2.2-point average improvement and consistent outperformance over SFT, on-policy RL, and hybrid baselines are stated without error bars, number of runs, data-split details, or statistical significance tests. This information is required to assess whether the delta can be confidently attributed to the forward-KL strategy distillation rather than variance or implementation differences.
  2. [Method (strategy extraction)] Method description (strategy extraction and reuse): the central claim that structured strategy descriptions are reusable across problems rests on the assumption that they generalize beyond source instances, yet no quantitative evidence (e.g., cross-problem transfer rates, strategy similarity metrics, or ablation removing strategy conditioning) is supplied to verify this reusability.
  3. [Method (forward-KL objective)] Forward-KL objective and proximal constraints: the paper asserts that the token-level forward-KL with proximal constraints transfers only beneficial shifts without instability or unintended bias, but reports no divergence metrics, policy-collapse diagnostics, or ablation isolating the proximal term. Without these checks the selective-distillation explanation for the observed gains remains unverified.
minor comments (2)
  1. [Method] The abstract and method sections would benefit from an explicit equation defining the token-level forward-KL objective and the form of the proximal constraint.
  2. [Experiments] Figure or table captions should clarify whether reported scores are means over multiple seeds or single-run results.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback. We address each major comment below with clarifications and commit to revisions that will strengthen the verification of our claims without misrepresenting the current manuscript.

read point-by-point responses

  1. Referee: [Abstract / experimental results] Abstract and experimental results section: the reported 2.2-point average improvement and consistent outperformance over SFT, on-policy RL, and hybrid baselines are stated without error bars, number of runs, data-split details, or statistical significance tests. This information is required to assess whether the delta can be confidently attributed to the forward-KL strategy distillation rather than variance or implementation differences.

    Authors: We agree that error bars, run counts, split details, and significance tests are necessary for robust interpretation. In the revised manuscript we will report results aggregated over multiple independent runs with standard deviations, specify the exact data splits and evaluation protocol, and include statistical significance tests for the reported improvements. revision: yes

  2. Referee: [Method (strategy extraction)] Method description (strategy extraction and reuse): the central claim that structured strategy descriptions are reusable across problems rests on the assumption that they generalize beyond source instances, yet no quantitative evidence (e.g., cross-problem transfer rates, strategy similarity metrics, or ablation removing strategy conditioning) is supplied to verify this reusability.

    Authors: The performance gains and complementary scaling with base-model size provide supporting evidence that the strategies are not merely instance-specific. To supply the requested quantitative verification, we will add an ablation that removes strategy conditioning and report strategy similarity metrics together with cross-problem transfer statistics in the revision. revision: yes

  3. Referee: [Method (forward-KL objective)] Forward-KL objective and proximal constraints: the paper asserts that the token-level forward-KL with proximal constraints transfers only beneficial shifts without instability or unintended bias, but reports no divergence metrics, policy-collapse diagnostics, or ablation isolating the proximal term. Without these checks the selective-distillation explanation for the observed gains remains unverified.

    Authors: We concur that explicit diagnostics would strengthen the selective-distillation argument. The revision will include token- and policy-level divergence measurements, policy-collapse diagnostics, and an ablation isolating the proximal constraints to confirm their contribution to stability and selectivity. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation uses external inputs and independent comparisons

full rationale

The paper's method extracts structured strategies from external strong-model responses, constructs autonomous and guided trajectories for comparison, and applies a token-level forward-KL objective with proximal constraints and adaptive weighting. No equations, fitted parameters, or predictions reduce by construction to the inputs (e.g., no self-definitional ratios or renamed fitted quantities). No load-bearing self-citations, uniqueness theorems from the same authors, or ansatzes smuggled via prior work are invoked in the abstract or description. The reported gains rest on experimental benchmarks against SFT, on-policy RL, and hybrid baselines rather than tautological redefinitions. This is the common case of a self-contained empirical proposal.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based solely on the abstract, the central claim rests on the unstated premise that strategy descriptions can be extracted as structured, reusable objects and that the forward-KL objective selectively isolates beneficial distributional shifts. No explicit free parameters, axioms, or invented entities are named in the provided text.

pith-pipeline@v0.9.1-grok · 5785 in / 1234 out tokens · 56248 ms · 2026-06-26T00:37:48.049542+00:00 · methodology

discussion (0)

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Reference graph

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