A Theory of Training Profit-Optimal LLMs

• URL: http://arxiv.org/abs/2605.16430v1
• Date: Thu, 14 May 2026 18:57:40 GMT
• Title: A Theory of Training Profit-Optimal LLMs
• Abstract summary: We develop an economic model for characterizing the rational behavior of an LLM training firm.<n>We analyze the profit problem for this model under compute-bound and data-bound regimes.
• Score: 12.802715423118316
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Scaling LLMs requires tremendous computational resources, and recent advances in AI have gone hand in hand with massive amounts of capital expenditure. While it is established that scaling up LLMs reliably increases model quality (quantified in terms of loss or downstream evaluations), it is unclear how these quality improvements translate to potential revenue, and whether revenue increases would offset costs of larger-scale training and inference. In this work, we develop an economic model for characterizing the rational behavior of an LLM training firm by combining scaling laws with microeconomic theory. Under our model of firm behavior, LLM quality can be increased with more parameters and training tokens, leading to more potential adoption by consumers, who each have a quality threshold for using the LLM. On the other hand, additional parameters and training tokens both incur additional costs. We analyze the profit maximization problem for this model under compute-bound and data-bound regimes. In the compute-bound regime, optimal model size and token budget track hardware efficiency $E$ (FLOPs/\$) at a near-linear rate; total training cost then scales sub-quadratically in $E$. Data efficiency improvements incentivize larger models and training expenditure. When we are limited to $D$ data, profit-optimal training expenditure scales as $D^2/E$, i.e, increase with data and decreases with hardware efficiency (as well as data efficiency). Finally, we analyze practical trends in training expenditure: current trends are consistent with our most permissive model variants in the compute-bound regime, but are not profit-optimal in the data-bound regime or assuming hardware advances will stall. Overall, our results provide a theory of profit-optimal LLM training, providing a foundation for engaging critically with industry statements and supporting long-term economic decision making.

Related papers

• Supervised Fine-Tuning vs. In-Context Learning: An Equilibrium Analysis of LLM Personalization under Congestion [52.722575491987904]
  We show that ICL and SFT dominate in different regimes, determined by an interplay between pretraining coverage and data signal-to-noise ratios.<n>We prove that offering both personalization methods never hurts the platform's maximal profits, despite potentially increasing computational load.
  arXiv  Detail & Related papers  (2026-07-15T21:17:42Z)
• Just-In-Time Reinforcement Learning: Continual Learning in LLM Agents Without Gradient Updates [53.3717573880076]
  We introduce Just-In-Time Reinforcement Learning (JitRL), a training-free framework that enables test-time policy optimization without any gradient updates.<n>JitRL maintains a dynamic, non-parametric memory of experiences and retrieves relevant trajectories to estimate action advantages on-the-fly.<n>Experiments on WebArena and Jericho demonstrate that JitRL establishes a new state-of-the-art among training-free methods.
  arXiv  Detail & Related papers  (2026-01-26T14:16:51Z)
• Thinking Augmented Pre-training [88.04395622064708]
  Thinking augmented Pre-Training is a universal methodology that augments text with automatically generated thinking trajectories.<n>This paper introduces a simple and scalable approach to improve the data efficiency of large language model (LLM) training by augmenting existing text data with thinking trajectories.
  arXiv  Detail & Related papers  (2025-09-24T14:45:13Z)
• Computational Economics in Large Language Models: Exploring Model Behavior and Incentive Design under Resource Constraints [1.00707850217229]
  Large language models (LLMs) are limited by substantial computational cost.<n>We introduce a "computational economics" framework that treats an LLM as an internal economy of resource-constrained agents.<n>We show that when computation is scarce, standard LLMs reallocate attention toward high-value tokens while preserving accuracy.
  arXiv  Detail & Related papers  (2025-08-14T07:55:45Z)
• Predictable Scale: Part II, Farseer: A Refined Scaling Law in Large Language Models [62.3458061002951]
  We introduce Farseer, a novel and refined scaling law offering enhanced predictive accuracy across scales.<n>By systematically constructing a model loss surface $L(N,D)$, Farseer achieves a significantly better fit to empirical data than prior laws.<n>Our methodology yields accurate, robust, and highly generalizable predictions, demonstrating excellent extrapolation capabilities.
  arXiv  Detail & Related papers  (2025-06-12T17:59:23Z)
• From Large to Super-Tiny: End-to-End Optimization for Cost-Efficient LLMs [23.253571170594455]
  Large Language Models (LLMs) have significantly advanced artificial intelligence.<n>This paper introduces a three-stage cost-efficient end-to-end LLM deployment pipeline.<n>It produces super-tiny online models with enhanced performance and reduced costs.
  arXiv  Detail & Related papers  (2025-04-18T05:25:22Z)
• Cost-Optimal Grouped-Query Attention for Long-Context Modeling [45.981681856747365]
  Grouped-Query Attention (GQA) is a widely adopted strategy for reducing the computational cost of attention layers in large language models.<n>We analyze the relationship among context length, model size, GQA configuration, and model loss.<n>We propose a recipe for deriving cost-optimal GQA configurations.
  arXiv  Detail & Related papers  (2025-03-12T17:50:42Z)
• A Little Help Goes a Long Way: Efficient LLM Training by Leveraging Small LMs [74.35290684163718]
  A primary challenge in large language model (LLM) development is their onerous pre-training cost. This paper explores a promising paradigm to improve LLM pre-training efficiency and quality by leveraging a small language model (SLM)
  arXiv  Detail & Related papers  (2024-10-24T14:31:52Z)
• Understanding the Performance and Estimating the Cost of LLM Fine-Tuning [9.751868268608675]
  Fine-tuning Large Language Models (LLMs) for specific tasks in a cost-effective manner. In this paper, we characterize sparse Mixture of Experts (MoE) based LLM fine-tuning to understand their accuracy and runtime performance. We also develop and validate an analytical model to estimate the cost of LLM fine-tuning on the cloud.
  arXiv  Detail & Related papers  (2024-08-08T16:26:07Z)
• Assessing Economic Viability: A Comparative Analysis of Total Cost of Ownership for Domain-Adapted Large Language Models versus State-of-the-art Counterparts in Chip Design Coding Assistance [10.364901568556435]
  This paper presents a comparative analysis of total cost of ownership (TCO) and performance between domain-adapted large language models (LLM) and state-of-the-art (SoTA) LLMs.
  arXiv  Detail & Related papers  (2024-04-12T23:37:56Z)
• Unleashing the Power of Pre-trained Language Models for Offline Reinforcement Learning [50.9692060692705]
  This paper introduces $textbfLanguage Models for $textbfMo$tion Control ($textbfLaMo$), a general framework based on Decision Transformers for offline RL.<n>Our framework highlights four crucial components:.<n>Initializing Decision Transformers with sequentially pre-trained LMs, (2) employing the LoRA fine-tuning method,.<n>In particular, our method demonstrates superior performance in scenarios with limited data samples.
  arXiv  Detail & Related papers  (2023-10-31T16:24:17Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.