让黑盒大模型精准调控决策，实现细粒度性能调节

Black-box Large Language Models (LLMs) provide practical and accessible alternatives to other machine learning methods, as they require minimal labeled data and machine learning expertise to develop solutions for various decision making problems. However, for applications that need operating with constraints on specific metrics (e.g., precision $\geq$ 95%), decision making with black-box LLMs remains unfavorable, due to their low numerical output cardinalities. This results in limited control over their operating points, preventing fine-grained adjustment of their decision making behavior. In this paper, we study using black-box LLMs as classifiers, focusing on efficiently improving their operational granularity without performance loss. Specifically, we first investigate the reasons behind their low-cardinality numerical outputs and show that they are biased towards generating rounded but informative verbalized probabilities. Then, we experiment with standard prompt engineering, uncertainty estimation and confidence elicitation techniques, and observe that they do not effectively improve operational granularity without sacrificing performance or increasing inference cost. Finally, we propose efficient approaches to significantly increase the number and diversity of available operating points. Our proposed approaches provide finer-grained operating points and achieve comparable to or better performance than the benchmark methods across 11 datasets and 3 LLMs.