Budget-Aware LLM Discovery via Cost-Calibrated Frontier Utility

Source

• Source name: arXiv
• Source kind: paper
• Authors / organization: Yansen Zhang, Yilu Liu, Tianyu Liu, Jiamin Chen, Xiaokun Zhang, Kai Xie, Xue Liu, Chen Ma, Yiyan Qi
• Venue: arXiv: cs.LG
• Published: 2026-07-29
• Collected: 2026-07-30
• URL: http://arxiv.org/abs/2607.26828v1
• PDF: https://arxiv.org/pdf/2607.26828v1
• DOI: UNKNOWN

Plain-Language Brief

Researchers have developed a new method for controlling large language models during scientific discovery tasks. The method, called CostAda, takes into account the costs associated with each action in addition to the progress made, unlike previous methods which only consider score progress. This new approach allows the model to make more informed decisions about where to focus its search and how much budget to allocate, resulting in better performance on twelve out of sixteen benchmark-backbone pairs under GLM-5 and GPT-5.4.

What the Document Says

• The paper discusses a new adaptive controller for large language models called CostAda.
• CostAda is designed to take into account the costs associated with each action during search, in addition to progress.
• Previous controllers only considered score progress without considering costs.
• The utility used by CostAda is called cost-calibrated frontier utility.
• This utility values frontier progress relative to realized action cost and remaining budget.
• CostAda controls local exploration intensity, frontier allocation, and budgeted tactic intervention based on this signal.
• With this approach, costs and remaining budget shape the search rather than serving only as accounting variables or a stopping rule.

Key Concepts Mentioned

• Large language models
• Adaptive controller
• Cost-calibrated frontier utility
• Search actions
• Token costs
• Frontier progress
• Budget allocation

Claims Made by the Document

• Existing adaptive discovery controllers assign credit based only on score progress.
• Cost-blind credit can forfeit all but a vanishing fraction of attainable quality as frontiers multiply and costs diverge.
• CostAda reaches the strongest baseline's full-budget quality with at most half the budget on twelve of sixteen benchmark--backbone pairs.

Evidence Used

• The paper provides details about the new adaptive controller CostAda and its design.

Methods / Approach

• CostAda uses cost-calibrated frontier utility to control the search.

Limitations Stated by the Authors

Not stated in source.

Limitations Noted by the Agent

Agent interpretation — not from the source.

It is unknown if there are any limitations to the method proposed by the authors as they are not explicitly mentioned in the text.

Open Questions

• What specific benchmarks were used in the experiments?
• Were there any other methods tested for comparison?

Notes for Future Q&A

May include interpretation. Labeled where it does.

• The paper does not provide specific details about the benchmarks used in the experiments.
• It is unclear if other methods were tested for comparison.

Raw Abstract / Excerpt

Large language models increasingly support scientific and algorithmic discovery through inference-time search over evaluated candidates. Existing adaptive discovery controllers assign credit based only on score progress, even though prompt length, retries, and guidance calls cause search actions to incur different token costs. We prove that cost-blind credit can forfeit all but a vanishing fraction of attainable quality as frontiers multiply and costs diverge. Under a fixed search-side token budget, the controller must decide which frontier is improving and whether its gain justifies the realized cost before the budget is exhausted. We introduce \textbf{CostAda}, a cost-calibrated adaptive controller built around \emph{cost-calibrated frontier utility}. The utility values frontier progress relative to realized action cost and conditions that credit on the remaining budget. CostAda uses this signal to control local exploration intensity, frontier allocation, and budgeted tactic intervention. Cost and remaining budget therefore shape the search rather than serving only as accounting variables or a stopping rule. CostAda reaches the strongest baseline's full-budget quality with at most half the budget on twelve of sixteen benchmark--backbone pairs while achieving the strongest mean final quality on all eight benchmarks under GLM-5 and GPT-5.4.