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.

FitText: Evolving Agent Tool Ecologies via Memetic Retrieval

A semantic gap separates how users describe tasks from how tools are documented. As API ecosystems scale to tens of thousands of endpoints, static retrieval from the initial query alone cannot bridge this gap: the agent's understanding of what it needs evolves during execution, but its tool set does not. We introduce FitText, a training-free framework that makes retrieval dynamic by embedding it directly in the agent's reasoning loop. FitText generates natural-language pseudo-tool descriptions as retrieval probes, refines them iteratively using retrieval feedback, and explores diverse alternatives through stochastic generation. Memetic Retrieval adds evolutionary selection pressure over candidate descriptions, guided by a tool memory that avoids redundant search. On ToolRet (43k tools, 4 domains), FitText improves average retrieval rank from 8.81 to 2.78; on StableToolBench (16,464 APIs), it achieves a 0.73 average pass rate--a 24-point absolute gain over static query retrieval. The gains transfer across base models capable of acting as competent semantic operators; under weaker base models, Memetic's evolutionary search inverts--amplifying noise rather than refining signal--surfacing model capacity as a prerequisite for evolutionary tool exploration.