推理的影子價格：大型語言模型最優預算分配的經濟學視角

摘要

推理時擴展已成為提升大型語言模型效能的關鍵途徑，然而實際部署卻受到嚴格計算預算的限制。在本研究中，我們將推理預算分配表述為受經濟原則支配的全局約束優化問題。透過以平移突增函數建模每次查詢的推理效用，我們推導出基於全局影子價格的最優分配策略，該價格在資源稀缺條件下使邊際效用達到均衡。基於此理論，我們提出「約束潛在效用均衡推理分配」（CLEAR）。該方法執行理性捨棄，並將資源從無償付能力查詢重新分配至接近其湧現閾值的可解查詢。在多種不同流量模式的推理任務上進行的廣泛實驗表明，CLEAR顯著改善了總令牌成本與平均準確率之間的帕累托前沿。在資源稀缺情境下，與均勻分配相比，CLEAR實現了高達三倍的全局準確率提升。

English

Inference-time scaling has emerged as a critical avenue for enhancing Large Language Models' performance, yet real-world deployment is constrained by strict computational budgets. In this work, we formulate inference budget allocation as a global constrained optimization problem governed by economic principles. By modeling per-query reasoning utility with a shifted-surge function, we derive an optimal allocation policy based on a global shadow price that equilibrates marginal utility under resource scarcity. Based on this theory, we propose Constrained Latent-utility Equilibrium Allocation for Reasoning (CLEAR). It performs rational abandonment and reallocates resources from insolvent queries to solvable queries near their emergence thresholds. Extensive experiments on several reasoning tasks with different traffic streams demonstrate that CLEAR significantly improves the Pareto frontier of total token cost versus mean accuracy. In resource-scarce regimes, CLEAR achieves up to a 3x improvement in global accuracy compared to uniform allocation.