Can We Afford The Perfect Prompt? Balancing Cost and Accuracy with the Economical Prompting Index

TL;DR

The paper introduces the Economical Prompting Index (EPI), a cost-aware metric that blends accuracy with token usage via $EPI(A,C,T) = A \times e^{(-C \times T)}$ to guide prompting choices under different resource constraints. It evaluates six prompting techniques across four datasets and ten language models, revealing that methods with the highest accuracy, such as Self-Consistency, often incur prohibitive token costs, while simpler approaches like Chain-of-Thought tend to remain more cost-effective as cost concerns rise. Model-agnostic analyses show rapid declines in EPI for high-cost methods, whereas simpler prompts preserve efficacy under tighter budgets; model-specific results (e.g., Claude 3.5 Sonnet) indicate that gains from complex prompting are often incremental and statistically insignificant. Case studies demonstrate practical savings and trade-offs in real deployments, underscoring the value of EPI for choosing prompts that balance performance with expense. Overall, EPI provides a flexible tool to steer cost-efficient prompting research and deployment, with implications for task-specific resource constraints and real-world applications.

Abstract

As prompt engineering research rapidly evolves, evaluations beyond accuracy are crucial for developing cost-effective techniques. We present the Economical Prompting Index (EPI), a novel metric that combines accuracy scores with token consumption, adjusted by a user-specified cost concern level to reflect different resource constraints. Our study examines 6 advanced prompting techniques, including Chain-of-Thought, Self-Consistency, and Tree of Thoughts, across 10 widely-used language models and 4 diverse datasets. We demonstrate that approaches such as Self-Consistency often provide statistically insignificant gains while becoming cost-prohibitive. For example, on high-performing models like Claude 3.5 Sonnet, the EPI of simpler techniques like Chain-of-Thought (0.72) surpasses more complex methods like Self-Consistency (0.64) at slight cost concern levels. Our findings suggest a reevaluation of complex prompting strategies in resource-constrained scenarios, potentially reshaping future research priorities and improving cost-effectiveness for end-users.

Figures (20)

• Figure 1: Economical Prompting Index (EPI) for GPT-4 across datasets, comparing no cost concern (C = 0) and moderate cost concern (C = 0.0005) scenarios. Prompt rankings shift when considering both accuracy (ACC) and token cost (TC).
• Figure 2: Graph of the token count $T$ against the EPI given the demonstrative weight classes $C$, for $A=1$.
• Figure 3: EPI by prompt method on GSM8K, relative to cost concern & averaged across all models
• Figure 4: EPI by prompt method on Claude 3.5 Sonnet, relative to cost concern & averaged across all tasks
• Figure 5: EPI comparison between Chain-of-Thought and standard prompting, given the parameters in Case Study 1.