Teaching Agents in their Own Style: Blackbox Teacher Distillation for Web Agents

Md Farhan Ishmam; Kenneth Marino

cs.AIOct 14, 2026

Teaching Agents in their Own Style: Blackbox Teacher Distillation for Web Agents

Authors: Md Farhan Ishmam, Kenneth Marino

Organizations: Kahlert School of Computing, University of Utah

Abstract

Frontier web agents using closed models have high inference and computational costs. Smaller open models can be an alternative, but to be performant, they require training supervision from a human or teacher model. Token-level teacher distillation is not an option for closed teachers as it needs access to the model's logits. The standard approach is to imitate teacher demonstrations offline, but it trains the student on states it has never visited, and in a style it does not write in. We introduce WebKD, where the teacher is the editor of the student's failures. Given a failed episode, the teacher finds the first point of mistake, and rewrites the student's reasoning traces, harness states, and actions from that point onward. The editing reveals that the teacher's corrections can be more surprising to the student than the student's own text. WebKD instead aims to edit minimally. In the data space, the teacher writes each correction in the student's style. In the objective space, the reasoning is weighted by its contribution to the action. A role-asymmetric KL anchor allows the corrected action to move freely while keeping the reasoning near the student's prior. On the TimeWarp benchmark, WebKD students gain about 5.5-10.7 pp over behavior cloning, outcome-reward RL, and teacher editing baselines. The performance transfers to unseen versions and to the live web in the OnlineMind2Web benchmark. WebKD opens a new way of distilling black-box models to improve the capabilities of open-weight web agents.

Figures & tables

Figure 1: Overview of WebKD . (Top) At step $t$ , the harness generates the observation history from the goal, accessibility tree, and previous responses. The web agent emits a five-component response conditioned on the observation history. The T hink, P lan, and S tep components carry their reasoning and running plan, the M emory component reads from and writes to the scratchpad memory, and only the A ction component is executed in the web environment, which returns the next observation. (Bottom) The student is behavior-cloned on the teacher’s rollouts (P1) and then generates rollouts from the training tasks (P2) . The teacher localizes each failure at $t^{\prime}$ (P3) and rewrites the faulty trajectory suffix in the student’s style (P4) . The resulting corpus $\mathcal{D}$ trains the student under action informativeness weighing, and KL anchored objective of § 3.3.1 –§ 3.3.2 .

Panel of Figure 2 — Figure 2: The perplexity premium by response components against the student’s continuations, the teacher’s raw corrections, and the WebKD ’s corpus with in-context edits.

Panel of Figure 3 — Figure 3: Edits for the same student step. The raw teacher edit replaces the student’s action but rewrites the plan in its own style. The style-conditioned edit keeps the student’s nested plan format. Values in brackets give the span weight $v_{s}$ . $\langle\mathrm{\textbf{T}}\rangle$ : think, $\langle\mathrm{\textbf{P}}\rangle$ : plan, $\langle\mathrm{\textbf{M}}\rangle$ : memory, $\langle\mathrm{\textbf{A}}\rangle$ : action.

Model	Baseline	v1	v2	v3	v4	v5	v6 (seen)
–	Teacher (GPT-5.5)	$71.8_{\pm 4.43}$	$71.8_{\pm 4.43}$	$68.0_{\pm 4.60}$	$68.0_{\pm 4.60}$	$69.9_{\pm 4.52}$	$70.9_{\pm 4.58}$
Qwen 3.5 4B	Zero-Shot	$1.0_{\pm 0.57}$	$1.0_{\pm 0.57}$	$0.3_{\pm 0.31}$	$1.6_{\pm 0.71}$	$0.0_{\pm 0.00}$	$1.0_{\pm 0.57}$
	Behavior Cloning	$10.7_{\pm 1.76}$	$9.4_{\pm 1.66}$	$9.7_{\pm 1.68}$	$10.7_{\pm 1.76}$	$5.2_{\pm 1.26}$	$9.7_{\pm 1.68}$
	Behavior Cloning (TW)	$27.5_{\pm 2.54}$	$28.5_{\pm 2.57}$	$27.8_{\pm 2.55}$	$26.2_{\pm 2.50}$	$28.2_{\pm 2.56}$	$29.8_{\pm 2.60}$
	m-GRPO	$30.1_{\pm 2.62}$	$27.2_{\pm 2.54}$	$26.2_{\pm 2.50}$	$28.2_{\pm 2.56}$	$30.1_{\pm 2.61}$	$30.4_{\pm 2.62}$
	Self/Student Edit	$25.2_{\pm 2.47}$	$19.4_{\pm 2.25}$	$27.2_{\pm 2.53}$	$24.3_{\pm 2.56}$	$23.3_{\pm 2.61}$	$23.6_{\pm 2.62}$

Table 1: Success rate (%) on the TimeWarp test split, in domain on v6 and on the five held-out versions v1–v5. Results are averaged over three runs with the standard error as the subscript.

Table 6

Panel of Figure 6 — Figure 6: Change in action distribution before and after teacher distillation using WebKD for the Qwen-3.5 4B baseline.

Appendix figures & tables4 assets

Supplementary material from the paper’s appendix.

Appendix

Hyperparameter	Value
fine-tuning	full-parameter, from the seed checkpoint
learning rate	$1\times 10^{-5}$ , cosine decay, warmup ratio $0.1$
epochs	$2$
context cutoff	$20{,}480$ tokens
batch	$1$ per device $\times$ $16$ -step gradient accumulation (effective $16$ )
precision	bf16, gradient checkpointing

Appendix

Table 4: Training hyperparameters for the combined objective.

Panel of Figure 7 — Figure 7: Behavior cloning over more epochs doesn’t improve the success rate, as it flattens at $\sim 25\%$ , whereas WebKD continues to improve and peaks at the 3rd total epoch for the Qwen-3.5 9B model. WebKD is trained from the first epoch of the BC seed.

Figure 8: Failure mode analysis of Qwen3.5-4B. Each bar assigns every evaluation trajectory of a method to exactly one outcome for the $103\times 3=309$ tasks.

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Distilling capable language-model agents into smaller models requires aligning the student's behavior with the teacher's. This raises a fundamental question: at which states and at what granularity should this alignment be performed? Offline imitation provides dense but token-specific supervision and can suffer from state-distribution mismatch. Token-level on-policy distillation (OPD) addresses this mismatch but typically requires teacher token probabilities and compatible tokenization. We argue that semantic actions provide a natural unit of supervision for agent distillation. We introduce ActionOPD, an action-level on-policy distillation method motivated by maximizing expected teacher-action likelihood at student-encountered states. At each such state, ActionOPD samples actions from both the student and a black-box teacher, rewarding student actions according to their semantic agreement with the sampled teacher actions. Through policy optimization, ActionOPD aligns the student's action-level behavior with the teacher's decisions without requiring reproduction of teacher-written reasoning or access to teacher token probabilities. Training Qwen3-4B and Qwen3-8B with two teachers on diverse, curated tool-use tasks yields average gains of 3.3-6.9 percentage points across four out-of-distribution benchmarks. ActionOPD scales favorably with student size and teacher capability, without requiring the teacher and student to share a model family or tokenizer. On

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