The Shadow Price of Reasoning: Economic Perspective on Optimal Budget Allocation for LLMs
On the map: LLM reasoning → Test-time compute and efficient thinking
Abstract (arXiv)
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.
Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning. Builds on 20 of its 22 references that are in the map. First posted on arXiv 2 Jun 2026.
Builds on
20 of 22 references.
Closest ancestors · 8
Same direction, newest first
- 2026Beyond Test-Time Compute Strategies: Advocating Energy-per-Token in LLM Inference4 Mar
- 2025AdapThink: Adaptive Thinking Preferences for Reasoning Language Model23 Jun
- 2025SelfBudgeter: Adaptive Token Allocation for Efficient LLM Reasoning16 May
- 2025L1: Controlling How Long A Reasoning Model Thinks With Reinforcement Learning6 Mar
- 2025s1: Simple test-time scaling31 Jan
- 2024Token-Budget-Aware LLM Reasoning24 Dec
- 2024Make Every Penny Count: Difficulty-Adaptive Self-Consistency for Cost-Efficient Reasoning24 Aug
- 2024Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters6 Aug
Other references · 12
- 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,302
- 2025Qwen3 Technical Reportcited by 8,195
- 2023Efficient Memory Management for Large Language Model Serving with PagedAttentioncited by 5,767
- 2021Convex optimizationcited by 2,479
- 2024Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvementcited by 1,057
- 2024Large Language Monkeys: Scaling Inference Compute with Repeated Samplingcited by 946
- 2023FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performancecited by 791
- 2024RouteLLM: Learning to Route LLMs with Preference Datacited by 633
- 2023FlexGen: High-Throughput Generative Inference of Large Language Models with a Single GPUcited by 567
- 2024Mixture-of-Depths: Dynamically allocating compute in transformer-based language modelscited by 242
- 2025DeepSeek-R1 Thoughtology: Let's think about LLM Reasoningcited by 91
- 2023System 2 Attention (is something you might need too)cited by 85
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Citing papers per year: 2026: 2.
2 papers.
Similar, not cited
Close in wording, no citation either way
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- 2024Inference Scaling vs Reasoning: An Empirical Analysis of Compute-Optimal LLM Problem-Solving
- 2025Plan and Budget: Effective and Efficient Test-Time Scaling on Reasoning Large Language Models
- 2025A Theory of Inference Compute Scaling: Reasoning through Directed Stochastic Skill Search
- 2026Keep, Customize, or Exit: Default Design and Token Pricing in LLM Reasoning Services