Rethinking Relative Policy Differences Transfer of On-Policy Distillation

Rong Wu; Daocheng Fu; Yu Yang; Xuemeng Yang; Siqi Li; Shu Zou; Yao Zhu; Botian Shi

cs.LGOct 9, 2026

Rethinking Relative Policy Differences Transfer of On-Policy Distillation

Authors: Rong Wu, Daocheng Fu, Yu Yang, Xuemeng Yang, Siqi Li, Shu Zou, Yao Zhu, Botian Shi,

Organizations: Zhejiang University · Shanghai Artificial Intelligence Laboratory · Fudan University · The Australian National University ·

Abstract

On-policy distillation (OPD) trains a target policy on its own rollouts using token-level supervision from a stronger teacher, but typically relies on the teacher being substantially more capable than the target. Recent work relaxes this requirement by transferring the relative policy difference between an expert and a reference policy rather than the expert's absolute distribution. Yet it remains unclear which differences provide useful supervision and which targets can benefit from them. We develop a unified view in which the log-probability ratio between a proxy expert and a proxy reference defines an implicit reward for KL-regularized policy optimization. This formulation induces an on-policy update for the target, recovers conventional OPD as a special case, and enables any-to-any transfer across models that differ in scale, training stage or generation. Our systematic experiments yield three findings. First, a stronger expert is not necessarily a better source of supervision: differences induced by task-specific training, including reinforcement learning and supervised fine-tuning, transfer consistently, whereas those arising from model scale alone transfer weakly or not at all. Second, the expert and reference serve complementary roles: the expert provides the capability to be transferred, while the reference filters out shared behavior and isolates the relevant residual. Third, even a useful difference does not transfer to every target: success requires the induced update to move the target toward the expert and generalize beyond sampled rollouts. Raw policy distance does not predict transferability, whereas an appropriate reference can rescue otherwise unsuccessful transfer. These results characterize when relative policy differences provide effective supervision for OPD.

Figures & tables

Method	$\pi_{\phi}^{+}$	$\pi_{\phi}$	$\pi_{\mathrm{ref}}$	$\alpha/\beta$	Advantage
OPD	$T^{+}$	$S$	$S$	$1$	$\log\pi_{T^{+}}-\log\pi_{\theta}$
ExOPD	$T^{+}$	$S$	$S$	$\lambda$	$\lambda(\log\pi_{T^{+}}-\log\pi_{S})-(\log\pi_{\theta}-\log\pi_{S})$
Relative Policy Transfer	$T^{+}$	$T$	$S$	$\lambda$	$(\log\pi_{T^{+}}-\log\pi_{T})-\lambda(\log\pi_{\theta}-\log\pi_{S})$

Table 1: Existing OPD methods as special cases of any-to-any policy transfer (Eq. 7 ). Here,

T^{+}

T

, and

S

denote the teacher expert, teacher base, and student base, respectively.

Source	Proxy expert / reference	Proxy performance ( $G_{P}$ )	Target performance ( $G_{T}$ )	$K_{\mathrm{Induced}}$
Task-optimized differences
RL	Qwen3-1.7B-RL / Qwen3-1.7B	$8.92\!\rightarrow\!25.15$ ( $+16.23$ )	$18.43\!\rightarrow\!28.21$ ( $+9.78$ )	0.0773
RL	Qwen3-4B-RL / Qwen3-4B	$17.82\!\rightarrow\!44.71$ ( $+26.89$ )	$18.43\!\rightarrow\!45.27$ ( $+26.84$ )	0.1066
RL	Skywork-7B / Qwen2.5-7B	$1.79\!\rightarrow\!43.93$ ( $+42.14$ )	$18.43\!\rightarrow\!50.66$ ( $+32.23$ )	0.2292
RL †	Qwen3-4B-RL / Qwen3-1.7B	$8.92\!\rightarrow\!44.71$ ( $+35.79$ )	$18.43\!\rightarrow\!44.28$ ( $+25.85$ )	0.3531
SFT	Qwen3-4B-SFT / Qwen3-4B	$17.82\!\rightarrow\!36.03$ ( $+18.21$ )	$18.43\!\rightarrow\!36.62$ ( $+18.19$ )	0.1725

Table 2: Transfer results for policy differences from different sources, with Qwen3-8B fixed as the target. † Alternative reference: the proxy reference is not the expert’s training origin.

Panel of Figure 1 — Figure 1: Transferability across sources of policy difference.

Proxy expert	Proxy reference	Proxy performance ( $G_{P}$ )	Target performance ( $G_{T}$ )	$K_{\mathrm{Base}}$	$R_{\mathrm{perf}}$	$\mathcal{O}_{E,R}$
Varying the expert; reference = Qwen3-4B-Base
Qwen3-8B	Qwen3-4B-Base	$17.82\!\rightarrow\!18.43$ ( $+0.61$ )	$18.43\!\rightarrow\!17.40$ ( $-1.03$ )	0.0533	$-1.680$	–
Qwen3-14B	Qwen3-4B-Base	$18.43\!\rightarrow\!19.54$ ( $+1.72$ )	$18.43\!\rightarrow\!18.45$ ( $+0.02$ )	0.0550	$0.016$	–
Qwen3-4B-SFT	Qwen3-4B-Base	$17.82\!\rightarrow\!36.03$ ( $+18.21$ )	$18.43\!\rightarrow\!36.62$ ( $+18.19$ )	0.0708	0.999	–
Qwen3-4B-Early-RL	Qwen3-4B-Base	$17.82\!\rightarrow\!39.91$ ( $+22.09$ )	$18.43\!\rightarrow\!40.85$ ( $+22.42$ )	0.0465	1.015	–
Qwen3-4B-RL	Qwen3-4B-Base	$17.82\!\rightarrow\!44.71$ ( $+26.89$ )	$18.43\!\rightarrow\!45.27$ ( $+26.84$ )	0.0484	0.998	0.839

Table 3: Effects of the proxy expert and reference on transfer . The shaded row is equivalent to standard OPD. Full policy-distance statistics are in Appendix B .

Figure 3: Effects of the proxy expert and reference on transfer. Qwen3-8B is fixed as the target.

Proxy Expert	Proxy Reference	Target	$K_{\text{Base}}$	$G_{T}$	$R_{\mathrm{perf}}$	Avg
Qwen3-1.7B-RL	Qwen3-1.7B	Qwen3-1.7B	0.000	16.11	- 0.993	25.03
Qwen3-1.7B-RL	Qwen3-1.7B	Qwen3-4B	0.106	13.65	- 0.841	31.47
Qwen3-1.7B-RL	Qwen3-1.7B	Qwen3-8B	0.111	9.78	- 0.603	28.21
Qwen3-1.7B-RL	Qwen3-1.7B	Qwen2.5-7B	0.462	-1.64	-0.101	0 0.15
Qwen3-1.7B-RL	Qwen3-1.7B	Qwen2.5-7B-Ins	0.656	-1.69	-0.104	0 5.17
Qwen3-1.7B-RL	Qwen3-1.7B	Qwen2.5-7B-Math	0.628	-0.08	-0.005	0 0.69

Table 4: Transfer results across proxy pairs and targets. The shaded rows denote Qwen2.5-generation targets.

Figure 4: The outcome is not a function of policy distance. Performance realization ratio (left) and transferred math accuracy (right) against the proxy–target base KL.

Panel of Figure 5 — Figure 5: Benefiting targets move toward the proxy expert (fixed Qwen3-1.7B proxy pair).

Panel of Figure 6 — Figure 6: Failure is not undertraining, and matching the reference generation recovers the benefit.

			Math		Code
Proxy Expert	Proxy Reference	Target	Avg	$G_{T}$	Avg	$G_{T}$
Same-generation transfer (Qwen3 $\rightarrow$ Qwen3)
Qwen3-4B-RL	Qwen3-4B	Qwen3-8B	45.27	$+26.8$	56.44	$+2.3$
Qwen3-4B-RL	Qwen3-1.7B	Qwen3-8B	44.28	$+25.9$	56.03	$+1.9$
Cross-generation transfer (Qwen3 proxy $\rightarrow$ Qwen2.5 target)
Qwen3-4B-RL	Qwen3-4B	Qwen2.5-7B	0 0.05	$-1.7$	22.83	$-6.4$

Table 5: Representative successful and failed settings performance on both math and code.

Appendix figures & tables5 assets

Supplementary material from the paper’s appendix.

Appendix

Table 6: Base model and proxy expert performance.

Table 7: Configurations, validation results, and distributional and efficiency metrics for policy difference experiments.

Table 8: Configurations, validation results, and distributional and efficiency metrics for varying proxy reference while fixed proxy expert.

Table 9: Configurations, validation results, and distributional and efficiency metrics for varying proxy expert while fixed proxy reference.

Table 10: Configurations, validation results, and distributional and efficiency metrics for varying target while fixed useful differences.

On-Policy Distillation

On-policy distillation trains a model on its own outputs using teacher guidance, aligning supervision with the states it encounters at deployment.

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A key challenge in on-policy distillation (OPD) is extracting effective supervision from teacher knowledge. Supervision from token probabilities may underutilize internal knowledge, while direct hidden-state matching forces the student to shift to the teacher's feature space and complicates cross-architecture transfer. Inspired by contrastive learning's use of relationships between instances, we propose SimOPD to transfer teacher internal knowledge through response similarities. Specifically, SimOPD uses paired memory banks of student-generated responses to extract supervision from the teacher's internal representations as similarity distributions. The student then matches these distributions within its own representation space, retaining representational freedom and removing the need for cross-model projection. Extensive experiments show that SimOPD improves the overall average over the strongest baselines by up to 2.6 and 3.1 percentage points in same- and cross-architecture settings.

Abstract

On-Policy Distillation

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