What they did
The authors formulate routing among heterogeneous AI specialists as an instance of the classical Pandora’s Box problem: a router has uncertain estimates of each specialist’s expected return and must decide whether paying for a better estimate is worthwhile before assigning a query.
Under a Gaussian signal model, they derive closed-form value-of-information rules for a centralized system, called Pandora’s Router. They also introduce Pandora’s Bidder, a decentralized mechanism in which specialists decide independently whether to pay for self-assessment before accepting a proposed price, and evaluate the approaches in three settings: a multi-LLM benchmark, retrieval-augmented specialists, and models using different amounts of inference-time reasoning.
Key findings
- Pandora’s Router matched the routing quality of exhaustively applying the expensive value estimator, while consulting that estimator substantially less often.
- The policy adapts its inspection decision to the query, specialist, estimation uncertainty, and assessment cost rather than using a fixed evaluation budget.
- Value-of-information reasoning improved allocation efficiency in the decentralized setting when estimates of competing specialists were accurate.
- When those competing estimates were noisy, strategic self-assessment could raise one specialist’s utility at the expense of others, revealing a distributional cost not captured by aggregate efficiency alone.
Why it matters
AI systems increasingly choose among models, retrieval pipelines, and reasoning budgets rather than invoking one fixed model. This work treats the cost of making that choice as part of the optimization problem, providing a principled way to reserve expensive evaluation for cases where it can plausibly change the assignment.
Caveats
The closed-form policy depends on a Gaussian signal model, so its behavior under misspecified, correlated, or heavy-tailed uncertainty remains an open question. The experiments cover three representative routing domains, but the abstract does not establish how the method scales to larger specialist pools or changing cost and performance distributions; the decentralized results also show that efficiency gains need not benefit all participants.