Research map / Large language models / Reasoning and chain of thought

The Shadow Price of Reasoning: Economic Perspective on Optimal Budget Allocation for LLMs

ICML 2026 · Large language models › Reasoning and chain of thought · approach: Test-time compute scaling · 0 citations (OpenAlex)

Read the paperCheck your idea against 108,967 papers

AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.

Frames batch-level inference token budget allocation as a constrained optimization over a shifted-surge latent utility, derives a Lambert W closed-form policy with a global shadow price found by bisection, and proposes CLEAR, a plug-and-play wrapper that abandons insolvent queries.

Problem

Under a fixed global token budget, uniform per-query generation limits waste compute on hard queries stuck in a zero-utility regime and on easy queries in diminishing-returns regimes; inference budget allocation across heterogeneous reasoning queries is needed.

Approach

Models per-query reasoning utility as an S-shaped shifted-surge function with an emergence threshold, derives a closed-form Lambert W allocation under a global shadow price (Lagrangian market clearing), and pairs it with a DeBERTa threshold predictor and rational abandonment of insolvent queries.

Key results

• Under a 256-token-per-query budget on the Mostly-Easy stream, CLEAR (Lambert) improves over Uniform by +24.0 accuracy points (33.0 vs 9.0).
• On code generation with Qwen2.5-Coder-7B under aligned best-of-4 budgets, CLEAR improves over Uniform by +6.3 on HumanEval+, +6.5 on MBPP+, and +3.6 on BigCodeBench.
• On Qwen3-30B-A3B-Instruct, CLEAR gains up to +2.4 accuracy over Uniform in the tightest budget setting, with smaller gains at larger budgets.

Surprising findings

• Gains from CLEAR shrink to near zero as budget grows (e.g., +0.0 on Mostly-Easy at 2048 tokens), and the Oracle upper bound is only modestly above CLEAR at larger budgets.
• Predictor-based proportional allocation without abandonment underperforms uniform allocation at low budgets, indicating that spreading tokens across all queries is harmful under scarcity.

Limitations

• Utility model is a fitted parametric approximation; α and β are treated as global hyperparameters rather than per-query, which the authors acknowledge as an assumption.
• Gap to oracle-level allocation remains, and performance depends on threshold predictor ranking quality; the paper reports accuracy degrades with predictor noise.
• Evaluation uses synthetic traffic streams built from a small oracle pool; the 30B model results show smaller gains (+0.2 to +2.4).

Experimental setup

Datasets: GSM8K MATH HumanEval MBPP

Benchmarks: MATH-500 AMC-23 AIME-24 AIME-25 Minerva OlympiadBench HumanEval+ MBPP+ BigCodeBench

Metrics: accuracy Pass@1 absolute accuracy gain

Baselines: Uniform allocation Proportional predictor allocation TALE-EP CLEAR (Heuristic) CLEAR (Auction) Oracle allocation

Builds on: TALE DeepSeek-R1 thoughtology

Closest papers by meaning

• Plan and Budget: Effective and Efficient Test-Time Scaling on Reasoning Large Language Models (ICLR 2026 · similarity 0.89)
• Every Rollout Counts: Optimal Resource Allocation for Efficient Test-Time Scaling (NeurIPS 2025 · similarity 0.89)
• Conformal Thinking: Risk Control for Reasoning on a Compute Budget (ICML 2026 · similarity 0.88)
• Training Language Models to Reason Efficiently (NeurIPS 2025 · similarity 0.88)
• Reasoning Is Not Free: Robust Adaptive Cost-Efficient Routing for LLM-as-a-Judge (ICML 2026 · similarity 0.88)
• Think Smarter not Harder: Adaptive Reasoning with Inference Aware Optimization (ICML 2025 · similarity 0.88)