LLM API调用成本高、选择困难，这篇论文为开发者提供了理论驱动的自适应查询策略，做模型编排或API调度的团队可以直接参考其方法优化成本与效果。
该论文提出了一种在线上下文潘多拉魔盒模型，用于自适应查询和选择LLM API。决策者在每个周期观察请求上下文，面临两阶段决策：查询阶段顺序调用API并产生输出相关成本，选择阶段从生成的输出中选一个部署并观察下游奖励。与经典模型不同，该模型输出反馈结构不直接揭示奖励。研究者直接建模保留索引，结合广义矩估计和UCB置信界，实现了维度相关的√T累积遗憾。
Online Pandora's Box for Contextual LLM Cascading
Motivated by Large Language Model (LLM) cascading, we propose an online contextual Pandora's Box model for adaptively querying and selecting LLM APIs. In each period, a decision-maker observes a request context and faces a two-phase decision problem. In the query phase, the decision-maker sequentially queries APIs, where each query reveals a generated output and the decision-maker incurs an (output-dependent) cost. In the selection phase, the decision-maker selects one of the generated outputs to deploy and observes only the downstream reward of the deployed output. This output-mediated feedback structure differs from classical online contextual Pandora's Box models, in which opening a box directly reveals its reward. Rather than estimating the full conditional output and cost distributions of each API, we directly model the reservation index and develop a learning approach for the query phase. Specifically, we impose a parametric structure on the contextual reservation index functions induced by the classical Weitzman's policy. Our policy combines generalized method of moments (GMM) type estimation of these reservation indices with UCB-style confidence bounds for both these indices and the shared output-level reward evaluator. Under regularity conditions, we prove that the resulting policy achieves dimension-dependent $\widetilde O(\sqrt T)$ cumulative regret over a horizon of $T$ periods.