Budget-Aware LLM Discovery via Cost-Calibrated Frontier Utility

2026-07-29

AI Summary

This work addresses the limitation of existing large language models in reasoning search, which often ignore the actual token costs of different actions and thus struggle to efficiently find high-quality solutions under a fixed budget. The authors propose CostAda, a novel approach that integrates token cost and remaining budget into frontier utility estimation, enabling a cost-calibrated adaptive controller that dynamically adjusts exploration intensity, frontier allocation, and policy intervention. By treating cost as a core guidance signal rather than merely a bookkeeping or termination criterion, CostAda achieves more efficient search. Experiments show that on 12 out of 16 benchmark–backbone combinations, CostAda matches or exceeds the full-budget performance of the strongest baseline using no more than half the budget; notably, it attains the best average final quality across all 8 benchmarks when paired with GLM-5 and GPT-5.4.

Abstract

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.

Problem

• large language models
• algorithmic discovery
• token cost
• adaptive control
• budget constraint

Innovation

• cost-calibrated frontier utility
• budget-aware search
• adaptive discovery controller
• token cost optimization
• CostAda