@inproceedings{gan-etal-2026-scaling,
    title = "Scaling Unverifiable Rewards: A Case Study on Visual Insights",
    author = "Gan, Shuyu  and
      Mooney, James  and
      Hao, Pan  and
      Wang, Renxiang  and
      Hong, Mingyi  and
      Wang, Qianwen  and
      Kang, Dongyeop",
    editor = "Liakata, Maria  and
      Moreira, Viviane P.  and
      Zhang, Jiajun  and
      Jurgens, David",
    booktitle = "Findings of the {A}ssociation for {C}omputational {L}inguistics: {ACL} 2026",
    month = jul,
    year = "2026",
    address = "San Diego, California, United States",
    publisher = "Association for Computational Linguistics",
    url = "https://preview.aclanthology.org/ingest-acl/2026.findings-acl.1724/",
    pages = "34537--34569",
    ISBN = "979-8-89176-395-1",
    abstract = "Large Language Model (LLM) agents can increasingly automate complex reasoning through Test-Time Scaling (TTS), an iterative refinement process guided by reward signals.However, many real-world tasks involve multi-stage pipelines whose final outcomes lack verifiable rewards or sufficient data to train robust reward models, making judge-based refinement prone to error accumulation across stages.We propose $\textbf{Selective TTS}$, a $\textit{process-based refinement}$ framework that scales inference across stages of a multi-agent pipeline, instead of repeatedly refining a single output over time as in prior work.By distributing compute across stages and pruning low-quality branches early using process-specific judgers, Selective TTS mitigates the judge drift and stabilizes refinement.Grounded in a data science workflow, we build an end-to-end multi-agent pipeline for generating visually insightful reports from a given dataset, and design a reliable LLM-based judge model that aligns with human experts (Kendall{'}s $\tau$=0.55) to evaluate them.Our proposed selective TTS then improves insight quality under a fixed compute budget, increasing mean scores from $\textbf{61.64}$ (baseline) to $\textbf{65.86}$ while reducing variance.We hope our findings serve as the first step toward scaling complex, open-ended tasks with unverifiable rewards like scientific discovery. Our code and generated reports are publicly available at https://minnesotanlp.github.io/insight-scaling-webpage."
}