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.<br>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.</p>\n","updatedAt":"2026-06-05T02:35:03.919Z","author":{"_id":"66da6555c1b41db982739497","avatarUrl":"/avatars/eaa2ddd88924b29afcca92f78ba2fdaf.svg","fullname":"XuWan","name":"Wanux","type":"user","isPro":false,"isHf":false,"isHfAdmin":false,"isMod":false,"isUserFollowing":false}},"numEdits":0,"identifiedLanguage":{"language":"en","probability":0.918767511844635},"editors":["Wanux"],"editorAvatarUrls":["/avatars/eaa2ddd88924b29afcca92f78ba2fdaf.svg"],"reactions":[],"isReport":false}}],"primaryEmailConfirmed":false,"paper":{"id":"2606.03092","authors":[{"_id":"6a20e40115100c5272a846be","user":{"_id":"66da6555c1b41db982739497","avatarUrl":"/avatars/eaa2ddd88924b29afcca92f78ba2fdaf.svg","isPro":false,"fullname":"XuWan","user":"Wanux","type":"user","name":"Wanux"},"name":"Xu Wan","status":"claimed_verified","statusLastChangedAt":"2026-06-04T12:39:56.266Z","hidden":false},{"_id":"6a20e40115100c5272a846bf","name":"Speed Zhu","hidden":false},{"_id":"6a20e40115100c5272a846c0","name":"Jianwei Cai","hidden":false},{"_id":"6a20e40115100c5272a846c1","name":"Guang Chen","hidden":false},{"_id":"6a20e40115100c5272a846c2","name":"XiMing Huang","hidden":false},{"_id":"6a20e40115100c5272a846c3","name":"Wiggin Zhou","hidden":false},{"_id":"6a20e40115100c5272a846c4","name":"Mingyang Sun","hidden":false}],"publishedAt":"2026-06-02T00:00:00.000Z","submittedOnDailyAt":"2026-06-05T00:00:00.000Z","title":"The Shadow Price of Reasoning: Economic Perspective on Optimal Budget Allocation for LLMs","submittedOnDailyBy":{"_id":"66da6555c1b41db982739497","avatarUrl":"/avatars/eaa2ddd88924b29afcca92f78ba2fdaf.svg","isPro":false,"fullname":"XuWan","user":"Wanux","type":"user","name":"Wanux"},"summary":"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.\n 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.","upvotes":4,"discussionId":"6a20e40215100c5272a846c5","githubRepo":"https://github.com/waunx/CLEAR","githubRepoAddedBy":"user","ai_summary":"Inference-time scaling is enhanced through constrained optimization that allocates computational resources based on economic principles, improving performance in resource-constrained environments.","ai_keywords":["inference-time scaling","Large Language Models","constrained optimization","economic principles","shifted-surge function","global shadow price","rational abandonment","resource allocation","Pareto frontier","token cost","mean accuracy"],"ai_summary_model":"Qwen/Qwen2.5-Coder-32B-Instruct","githubStars":0,"organization":{"_id":"61dcd8e344f59573371b5cb6","name":"PekingUniversity","fullname":"Peking University","avatar":"https://cdn-avatars.huggingface.co/v1/production/uploads/noauth/vavgrBsnkSejriUF4lXDE.png"}},"canReadDatabase":false,"canManagePapers":false,"canSubmit":false,"hasHfLevelAccess":false,"upvoted":false,"upvoters":[{"_id":"66da6555c1b41db982739497","avatarUrl":"/avatars/eaa2ddd88924b29afcca92f78ba2fdaf.svg","isPro":false,"fullname":"XuWan","user":"Wanux","type":"user"},{"_id":"6a224a4ecd21e88e42d642ed","avatarUrl":"/avatars/557089ade1e05a813f161543ad3cc8e0.svg","isPro":false,"fullname":"maya","user":"MayaXu","type":"user"},{"_id":"694a9cf75b10195accb88ad3","avatarUrl":"/avatars/cc6a711f521627ae675117376720ad0d.svg","isPro":false,"fullname":"Zhenghao Yang","user":"Flarinko","type":"user"},{"_id":"691708d48a7b85d49c5952a9","avatarUrl":"/avatars/bb64ee6969b40311a3cab6414890e331.svg","isPro":false,"fullname":"huangximing","user":"llm-hxm","type":"user"}],"acceptLanguages":["en"],"dailyPaperRank":0,"organization":{"_id":"61dcd8e344f59573371b5cb6","name":"PekingUniversity","fullname":"Peking University","avatar":"https://cdn-avatars.huggingface.co/v1/production/uploads/noauth/vavgrBsnkSejriUF4lXDE.png"},"markdownContentUrl":"https://huggingface.co/buckets/huggingchat/papers-content/resolve/2606/2606.03092.md"}">
The Shadow Price of Reasoning: Economic Perspective on Optimal Budget Allocation for LLMs
Published on Jun 2
· Submitted by XuWan on Jun 5 Abstract
Inference-time scaling is enhanced through constrained optimization that allocates computational resources based on economic principles, improving performance in resource-constrained environments.
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.
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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.
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