用数学语言精准定义多目标任务，让大模型更准确地完成推荐
UtilityMax Prompting: A Formal Framework for Multi-Objective Large Language Model Tasks
- 用数学公式构建任务框架，明确每个目标的权重与关系
- 在电影推荐任务中，精确度和NDCG指标均优于自然语言提示
- 适合需要多目标平衡的复杂决策场景，如个性化推荐
大模型任务的成功高度依赖于提示设计。现有方法多采用自然语言描述提示，当需同时满足多个目标时，易产生歧义。本文提出UtilityMax Prompting框架，将任务以形式化数学语言重构为影响图，其中大模型输出是唯一决策变量。定义基于条件概率分布的效用函数，指导大模型寻找最大化期望效用的答案。该方法迫使模型显式推理各目标成分，避免主观理解偏差。我们在MovieLens 1M数据集上，对Claude Sonnet 4.6、GPT-5.4和Gemini 2.5 Pro三款前沿模型进行验证，结果表明，在多目标电影推荐任务中，该方法在精度与归一化折现累积增益（NDCG）上持续优于自然语言基线。
原文摘要 · Abstract (English)
The success of a Large Language Model (LLM) task depends heavily on its prompt. Most use-cases specify prompts using natural language, which is inherently ambiguous when multiple objectives must be simultaneously satisfied. In this paper we introduce UtilityMax Prompting, a framework that specifies tasks using formal mathematical language. We reconstruct the task as an influence diagram in which the LLM's answer is the sole decision variable. A utility function is defined over the conditional probability distributions within the diagram, and the LLM is instructed to find the answer that maximises expected utility. This constrains the LLM to reason explicitly about each component of the objective, directing its output toward a precise optimization target rather than a subjective natural language interpretation. We validate our approach on the MovieLens 1M dataset across three frontier models (Claude Sonnet 4.6, GPT-5.4, and Gemini 2.5 Pro), demonstrating consistent improvements in precision and Normalized Discounted Cumulative Gain (NDCG) over natural language baselines in a multi-objective movie recommendation task.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。