DivOPD: Spread Wide, Look Close for Asynchronous On-Policy Distillation of Multi-turn Agents

Hanyang Wang; Zeyuan Liu; Zhengyu Chen; Jingqing Ruan; Chaoxu Pang; Zhongda Su; Wulin Xie; Zhizhao Zeng

cs.LGSep 28, 2026

DivOPD: Spread Wide, Look Close for Asynchronous On-Policy Distillation of Multi-turn Agents

Authors: Hanyang Wang, Zeyuan Liu, Zhengyu Chen, Jingqing Ruan, Chaoxu Pang, Zhongda Su, Wulin Xie, Zhizhao Zeng, +2 more

Organizations: University of Chicago · Meituan LongCat Interaction Team · University of the Chinese Academy of Sciences · The Hong Kong University of Science and Technology (Guangzhou)

Abstract

On-policy distillation (OPD) trains student agents through teacher supervision on their own interactions with an environment. However, in asynchronous multi-turn training, arrival-order batching can allow a few early or long rollouts to dominate learner updates while other valid rollouts become stale before being used, wasting already-generated experience. To address this problem, we introduce DivOPD, a simple learner-side batch-selection method that spreads a fixed turn budget across more rollouts and, within each rollout, prioritizes turns with larger cumulative teacher-student disagreement. Turns without usable teacher feedback are excluded. The per-turn loss and optimizer remain fixed; selection only changes which student-visited turns receive training weight. For no-progress rollouts, an optional extension briefly hands control to the teacher before returning it to the student. Across six teacher-student settings on the simulated ALFWorld, ScienceWorld, and WebShop benchmarks, with 1.5B-7B students, DivOPD raises cross-setting mean peak success rate from 77.4 to 84.4 and mean success over the last five evaluations from 71.5 to 78.6. It reaches all reported setting-specific targets with geometric-mean speedups of 1.84x in training tokens and 1.87x in learner GPU time relative to vanilla OPD. Teacher intervention further raises this last-five mean to 82.4 while retaining about 1.7x learner-GPU speedup over vanilla OPD. Code will be released at https://github.com/HanyangWang0418-oss/DivOPD.

Figures & tables

Figure 1: Batch composition in asynchronous multi-turn OPD. (A) Rollout workers enqueue variable-length interactions in arrival order. (B) When production outpaces learner consumption, early or long rollouts can fill the batch, include unscored rows, and leave others to expire as stale. (C) DivOPD composes batches on the learner side through the three stages in Section 3 : validity gate, rollout-first coverage, and within-rollout disagreement focus using $s(u)$ (Equation 2 ). (D) When rollouts repeatedly make no progress, bounded teacher recovery helps the student continue; teacher actions are excluded from the loss, and recovery is disabled at evaluation. Bottom: independent exploration and training, with periodic model synchronization and stale-row expiry.

ALFWorld	Qwen3-1.7B ( $T$ /Init: 87.86/7.86; $\tau{=}70$ )				Qwen3-4B ( $T$ /Init: 87.86/26.43; $\tau{=}80$ )
Method	Peak $\uparrow$	Final-5 $\uparrow$	Tok. $\uparrow$	GPU $\uparrow$	Peak $\uparrow$	Final-5 $\uparrow$	Tok. $\uparrow$	GPU $\uparrow$
Vanilla OPD	77.86	74.00 $\pm$ 3.18	1.00 $\times$	1.00 $\times$	86.43	84.57 $\pm$ 1.48	1.00 $\times$	1.00 $\times$
TCOD-F2B	72.86	68.43 $\pm$ 3.09	1.62 $\times$	1.63 $\times$	87.14	83.00 $\pm$ 1.28	1.49 $\times$	1.51 $\times$
TurnOPD	78.57	75.71 $\pm$ 2.72	1.77 $\times$	1.76 $\times$	87.14	86.43 $\pm$ 0.51	1.57 $\times$	1.59 $\times$
DivOPD-focus	80.00	71.00 $\pm$ 6.62	1.50 $\times$	1.46 $\times$	89.29	85.29 $\pm$ 3.10	1.69 $\times$	1.70 $\times$
DivOPD-base	74.29	72.86 $\pm$ 1.43	1.35 $\times$	1.35 $\times$	92.14	88.86 $\pm$ 2.29	1.27 $\times$	1.27 $\times$

Table 1: Main results. Peak/Final-5 are best-checkpoint/final-five mean SR (%);

\pm

is the standard deviation over the last five checkpoints. Headers give teacher/student-initial SR. Tok./GPU are

C_{\mathrm{vanilla}}(\tau)/C_{\mathrm{method}}(\tau)

for cumulative learner training tokens and trainer GPU-hours, respectively. Larger is better; a dash means that the method did not reach

\tau

. Red/purple mark best/second-best; DivOPD-focus is an uncontrolled reference.

Load	Reader	Rollout bs	Arrival/drain	Final SR $\uparrow$	nAUC@150 $\uparrow$	Stale rows $\downarrow$
Low	Vanilla OPD	2	0.77	52.1	25.0	240
Low	DivOPD-base	2	0.55	52.0	25.4	53
Medium	Vanilla OPD	6	1.35	53.6	25.3	8,035
Medium	DivOPD-base	6	0.88	56.5	26.0	4,237
High	Vanilla OPD	16	2.27	49.3	26.9	30,175
High	DivOPD-base	16	0.89	59.3	27.8	9,766

Table 2: Stress test under increasing asynchronous producer load. ALFWorld Qwen3-1.7B over 150 learner updates. Arrival/drain is the measured queue arrival rate divided by the learner drain rate; values above one indicate a growing backlog. SR and nAUC are percentages; stale rows are raw counts. Bold marks the better value within each load level.

Appendix figures & tables18 assets

Supplementary material from the paper’s appendix.

Appendix

	Input: update index $q$ ; pending turns $P$ ; rollout buffer $\mathcal{E}$ ; batch size $B$ ; pool multiplier $c$ ; initial per-rollout cap $k$ ; maximum staleness $\delta$ ; maximum pending age $W$ .
1	Set $v_{\min}\leftarrow\max(q-\delta,0)$ and remove every $u\in P$ with $\operatorname{version}(u)<v_{\min}$ .
2	Read $F$ from $\mathcal{E}$ with version at least $v_{\min}$ until $\|P\|+\|F\|=cB$ (or the read returns no more turns); set $C\leftarrow P\cup F$ .
3	Set $V\leftarrow\{u\in C:\textsc{Valid}(u)\}$ and permanently discard $C\setminus V$ . Stamp a fresh turn’s first-seen update as $q$ .
4	Group $V$ by rollout identifier $r$ . Order rollout groups by oldest first-seen update, breaking ties by $r$ .
5	Within every group, sort turns by descending $s(u)$ , breaking ties by $(r,t)$ . Initialize the selected set $S\leftarrow\varnothing$ and cap $h\leftarrow k$ .
6	Sweep the ordered rollout groups once. From each group append its highest ranked unselected turns until that group contributes $k$ turns or $\|S\|=B$ .

Appendix

Algorithm 1: DivOPD sampler ( trajectory_first with turn_signal=raw_kl_sum ). Table 3 lists the reported numerical settings.

Setting	Value
Learner batch size $B$	64 turn rows
Candidate-pool multiplier $c$	4 (at most 256 pending and fresh turns)
Maximum policy staleness $\delta$	2 model versions
Maximum pending age $W$	8 learner updates
Initial per-rollout cap $k$	ALFWorld 1.7B/4B: 4/4; WebShop 3B/7B: 5/4; ScienceWorld 1.5B/3B: 4/5
Per-turn loss settings	$\beta=1$ ; unit row weights

Appendix

Table 3: Shared sampler configuration. All methods use the same learner batch size. DivOPD-base and DivOPD share these sampler values; only their within-rollout selection differs.

Setting	Value
Optimizer	AdamW
Learning rate	$10^{-6}$ ; constant schedule; no warmup
Adam moments	$\beta_{1}=0.9,\ \beta_{2}=0.999$
Weight decay	$0.01$
Gradient-norm clipping	$1.0$
Optimizer batch	$N=64$ turn rows; seq-mean-token-mean (Equation 3 )

Appendix

Table 4: Shared optimizer configuration. These settings are fixed across all methods.

Environment	Student	Initial SR (%)
ALFWorld	Qwen3-1.7B	7.86
ALFWorld	Qwen3-4B	26.43
WebShop	Qwen2.5-3B-Instruct	1.56
WebShop	Qwen2.5-7B-Instruct	14.06
ScienceWorld	Qwen2.5-1.5B-Instruct	21.48
ScienceWorld	Qwen2.5-3B-Instruct	45.31

Appendix

Table 5: Student initialization, frozen teachers, and evaluation protocol. Initial SR is measured before the first learner update under the reported evaluation protocol; teacher SR uses the same fixed test episodes. Training responses are sampled at temperature

1.0

, and evaluation uses temperature

0.4

Training task types (17)	Held-out evaluation task types (13)
boil; melt; change-the-state-of-matter-of; use-thermometer; measure-melting-point-known-substance; power-component; test-conductivity; find-living-thing; find-plant; grow-plant; chemistry-mix; chemistry-mix-paint-secondary-color; lifespan-shortest-lived; identify-life-stages-2; inclined-plane-determine-angle; inclined-plane-friction-named-surfaces; mendelian-genetics-known-plant	freeze; measure-melting-point-unknown-substance; power-component-renewable-vs-nonrenewable-energy; test-conductivity-of-unknown-substances; find-non-living-thing; find-animal; grow-fruit; chemistry-mix-paint-tertiary-color; lifespan-longest-lived; lifespan-longest-lived-then-shortest-lived; identify-life-stages-1; inclined-plane-friction-unnamed-surfaces; mendelian-genetics-unknown-plant

Appendix

Table 6: ScienceWorld task-type split. Training and evaluation use disjoint task types. Within each type, we retain the first half of the official variation IDs before applying a fixed shuffle.

Setting	Method	Accuracy		Efficiency to $\tau$
		Peak $\uparrow$	Final-5 $\uparrow$	Updates $\downarrow$	Trainer GPU h $\downarrow$	GPU speedup $\uparrow$
ALFWorld Qwen3-4B $\tau{=}80$	Vanilla OPD	86.43	84.57 $\pm$ 1.48	184	13.51	1.00 $\times$
	TCOD-F2B	87.14	83.00 $\pm$ 1.28	182	8.95	1.51 $\times$
	TurnOPD	87.14	86.43 $\pm$ 0.51	161	8.50	1.59 $\times$
	DivOPD-focus	89.29	85.29 $\pm$ 3.10	148	7.97	1.70 $\times$
	DivOPD-base	92.14	88.86 $\pm$ 2.29	154	10.61	1.27 $\times$

Appendix

Table 7: Full results across six teacher–student settings. Peak SR is the best checkpoint; Final-5 is the mean

\pm

standard deviation over the last five evaluation checkpoints. Best values are highlighted in bold; second-best are underlined.

Design question	Component	DivOPD
How is each turn scored?	Learning signal	Unchanged (Eq. 1 )
How long can a rollout continue?	Rollout horizon	Unchanged
Who acts during the rollout?	Rollout policy	Changed only by DivOPD $+$ R (§ 3.4 )
Which turns enter a learner batch?	Batch selection	Changed by DivOPD (§ 3 )

Appendix

Table 8: What DivOPD changes. The core method changes batch selection; only the optional recovery extension changes rollout generation.

Setting	Method	Eff. rollouts	Top-1 tok.	Turns per	KL / token	Step time	Peak SR
		/ batch $\uparrow$	share $\downarrow$	rollout	$\downarrow$	(s) $\downarrow$	(%) $\uparrow$
ALFWorld 4B	Vanilla OPD	6.7	0.281	8.1	0.121	94.9	86.43
	TCOD-F2B	6.5	0.291	8.6	0.114	99.6	87.14
	DivOPD-focus	18.6	0.110	2.4	0.174	85.2	89.29
	DivOPD-base	12.5	0.136	3.9	0.111	97.8	92.14
	DivOPD	12.5	0.145	3.9	0.176	82.1	91.43

Appendix

Table 9: Full batch-composition diagnostics. Values are averaged over the final

40\%

of training; peak SR is repeated from Appendix Table 7 . Focus-only maximizes coverage in five settings, while DivOPD has the higher peak SR in five. Bold marks the best peak SR among the five methods shown, which exclude DivOPD

+

R. Figure 2 averages the first three diagnostics over the two student sizes per environment.

	Dropped share		Turn depth		Score/token
Setting	Turns	Grad. norm	Kept	Dropped	Kept	Dropped
ScienceWorld 3B	55%	40%	4.7	9.5	0.30	0.16
WebShop 3B	18%	12%	2.3	4.5	0.16	0.08

Appendix

Table 10: Focus retention audit (

k=5

, the initial cap used in Table 1 for these settings). Dropped gradient norm is the share of summed per-turn norms,

\sum_{t}\|g_{t}\|

, estimated by the sketch audit. The last four columns are means for kept and dropped turns.

Shared buffers: first 100 updates
	Never selected (%)			Gini
Composer	ALF	SciW	WS	ALF	SciW	WS
Vanilla OPD (arrival-order)	53.9	49.2	58.7	0.66	0.68	0.64
Top- $B$ (no rollout limit)	–	–	–	0.44	0.45	0.27
DivOPD-focus	15.0	10.2	3.4	0.33	0.32	0.20
DivOPD-base / DivOPD	14.2	11.0	7.1	0.30	0.32	0.12

Appendix

Table 11: Cumulative rollout utilization. Never selected is the share of valid rollouts contributing no trained turn; Gini measures concentration of selected-turn counts. ALF/SciW/WS denote ALFWorld/ScienceWorld/WebShop. The separate-buffer result is grouped below the shared-buffer comparisons and is not a matched control.

Setting	$\mathrm{max\_staleness}$	Mean age	Peak	Final ckpt.
ALFWorld 1.7B	2	1.69	77.86	73.57
	4	3.19	71.43	71.43
ScienceWorld 1.5B	2	1.68	66.02	66.02
	4	2.96	65.62	60.16

Appendix

Table 12: Vanilla OPD with a wider staleness window. Mean age of consumed rows in policy versions (arrival-order replay, dead rows included), peak and final-checkpoint SR (%). The

\mathrm{max\_staleness}=2

rows reuse the main vanilla runs in Table 1 ; the wider-window rows are separate auxiliary runs rather than paired reruns.

	Gradient projection			Cosine similarity
Composer	ALF	SciW	WS	ALF	SciW	WS
Arrival order †	1.74	0.75	1.32	0.97	0.49	0.61
Gate only	1.11	1.02	1.29	0.93	0.53	0.62
DivOPD-base	1.36	0.97	1.31	0.96	0.54	0.62
DivOPD	2.04	2.01	1.47	0.98	0.75	0.64
DivOPD-focus	3.12	1.66	1.50	0.99	0.67	0.65

Appendix

Table 13: Selected gradients versus the candidate-pool gradient. Means over 8 audited updates per environment. Projection is

\langle G,\hat{G}\rangle/\|G\|^{2}

; cosine similarity is

\cos(G,\hat{G})

. ALF/SciW/WS denote ALFWorld/ScienceWorld/WebShop. † Arrival order here draws from the finite-

k

composer’s pool and is not vanilla OPD. Sketch oracle selects and evaluates the

B

turns with the largest sketched

\langle G,g_{t}\rangle

, so it is an optimistic reference rather than a full-gradient oracle.

Depth	Outcome	Vanilla	$+$ Gate	$+$ Coverage	$+$ Focus
$<2$	Failure	3.2	3.8	6.1	10.6
$<2$	Success	17.6	20.7	14.3	15.8
$[2,4)$	Failure	3.1	3.6	6.1	8.5
$[2,4)$	Success	17.4	20.4	14.1	14.5
$[4,6)$	Failure	2.9	3.4	5.9	7.4
$[4,6)$	Success	13.1	15.3	9.7	9.7

Appendix

Table 14: Where selected turns come from in the ALFWorld 1.7B DivOPD replay. Share of selected turns (%), grouped by turn depth and rollout outcome. Each method column sums to approximately

100\%

after rounding; stages are added one at a time from left to right.

Setting	Trained tokens	Trainer GPU	Wall time (est.)
ALFWorld 4B	1.92 $\times$	1.94 $\times$	1.36 $\times$
ALFWorld 1.7B	2.05 $\times$	2.07 $\times$	1.28 $\times$
WebShop 3B	2.22 $\times$	2.22 $\times$	0.99 $\times$
WebShop 7B	1.77 $\times$	1.92 $\times$	0.83 $\times$
ScienceWorld 3B	1.62 $\times$	1.63 $\times$	1.22 $\times$
ScienceWorld 1.5B	1.54 $\times$	1.54 $\times$	1.27 $\times$

Appendix

Table 15: Resource efficiency to

\tau

. Vanilla-to-DivOPD ratios; larger is better. Trainer GPU time uses the two GPUs assigned to the learner. The wall estimate sums trainer-step and experience-read time. Its speedup differs from timestamp-based end-to-end measurement by at most

1.2\%

on the three settings whose timestamps were retained.

	DivOPD ( $k{=}3$ )		DivOPD-focus
Setting	scored/trained	not selected	scored/trained	not selected
ALFWorld 1.7B	2.77 $\times$	63.9%	2.89 $\times$	65.4%
ALFWorld 4B	2.73 $\times$	63.4%	2.93 $\times$	65.9%
ScienceWorld 1.5B	3.66 $\times$	72.6%	3.79 $\times$	73.6%
ScienceWorld 3B	3.41 $\times$	70.6%	3.60 $\times^{*}$	72.2%
WebShop 3B	1.89 $\times$	47.1%	1.86 $\times$	46.3%

Appendix

Table 16: Teacher tokens scored per token trained. Effective tokens; “not selected” is the share never entering an optimizer batch. This audit uses the

k=3

runs from Table 19 , not the per-setting caps of Table 1 . ∗ Two parallel 150-update trainer histories sharing one buffer, merged.

		Vanilla reader			Rollout-first selection
Environment	Model	Peak $\uparrow$	Best-5 $\uparrow$	Final $\uparrow$	Peak $\uparrow$	Best-5 $\uparrow$	Final $\uparrow$
ALFWorld	1.7B	78.57	73.86	78.57	80.00	77.71	78.57
WebShop	3B	75.00	68.44	71.09	78.12	74.06	68.75
ScienceWorld	1.5B	73.44	72.66	73.05	77.73	74.38	74.61

Appendix

Table 17: Matched candidate access. Both arms draw from the same

256

-turn stream; vanilla otherwise reads in arrival order. Best-5 averages the five best checkpoints; Final is SR at the common learner-version cutoff. These separate runs are not numerically comparable to Table 1 .

		Finite $k$ (DivOPD-base)		$k=\infty$ (no cap)
Environment	Model	Peak SR $\uparrow$	Final-5 SR $\uparrow$	Peak SR $\uparrow$	Final-5 SR $\uparrow$
ALFWorld	1.7B	74.29	72.86	73.57	65.14
ALFWorld	4B	92.14	88.86	90.00	87.71
WebShop	3B	78.12	73.12	75.00	65.47
WebShop	7B	88.28	78.44	87.62	81.09
ScienceWorld	1.5B	70.31	67.50	67.97	62.89

Appendix

Table 18: Matched-access cap comparison. Both arms use the same candidate-pool size, gate, ordering, pending rule, and within-rollout sampling; only the initial cap differs. SR is in percent.

Method	ALFWorld		WebShop		ScienceWorld
	1.7B	4B	3B	7B	1.5B	3B
TCOD-F2B	72.86	87.14	67.19	89.06	71.88	87.89
DivOPD ( $k=3$ )	87.14	90.00	71.09	91.41	77.73	85.55
DivOPD ( $k=4$ )	79.29	91.43	73.44	90.62	78.91	86.33
DivOPD ( $k=5$ )	79.29	91.43	78.12	88.28	75.78	88.28
DivOPD ( $k=6$ )	80.71	88.57	73.44	86.72	75.78	85.55

Appendix

Table 19: Sensitivity to the initial per-rollout cap

k

. Peak SR (%); TCOD-F2B is a reference. Best DivOPD values are highlighted, and second-best values are underlined.

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Open paper AskPDF arXiv

While on-policy distillation (OPD) reduces exposure bias by training student language models on their own rollouts, early student errors in long-horizon agentic scenarios can lead to contexts unfamiliar to the teacher. To improve trajectory quality, recent work on agentic OPD introduces teacher intervention into training rollouts by switching the executor between the student and the teacher. However, existing methods determine how much teacher intervention is needed---but not when. To address this limitation, we propose DASH-OPD (Discrepancy-Aware Switching with Hysteresis for OPD), the first agentic OPD method to perform adaptive, bidirectional executor switching. At each turn, DASH-OPD measures teacher--student discrepancy using a mean log-probability ratio over action tokens. Student-to-teacher ratios on student turns serve as drift signals, while teacher-to-student ratios on teacher turns serve as recovery signals. These signals are accumulated over multiple turns to form drift and recovery evidence, respectively. DASH-OPD switches executors when either type of evidence exceeds its corresponding switching threshold, introducing hysteresis that prevents rapid switching triggered by transient discrepancy fluctuations. Across three benchmarks and two student model sizes, DASH-OPD outperforms five baselines in all 14 task performance comparisons, while requiring the fewest interaction turns in nine of ten efficiency comparisons. Code, models, and training logs are available at https://github.com/Lucian1115/DASH-OPD

Abstract

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