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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.\n  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 stru","title":"Online Pandora's Box for Contextual LLM Cascading","url":"https://arxiv.org/abs/2606.07392","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.07392v1 Announce Type: new \nAbstract: 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.\n  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. 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