# The Pandora's Box Problem with Sequential Inspections

arXiv: https://arxiv.org/abs/2507.07508 · HTML: https://mlsanity.com/paper/2507.07508/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jul 2025.

## Built on by (most cited first, 4 of 4)

- [Re-FORC: Adaptive Reward Prediction for Efficient Chain-of-Thought Reasoning](https://mlsanity.com/paper/2511.02130/) (2025)
- [T-TAMER: Provably Taming Trade-offs in ML Serving](https://mlsanity.com/paper/2509.22992/) (2025)
- [Algorithmic Approaches to Sequential Decision-Making and Social Epistemology](https://mlsanity.com/paper/2607.20636/) (2026)
- [Can Labor Markets Function in the Age of AI? The Evaluation Bottleneck in Hiring](https://mlsanity.com/paper/2609.30058/) (2026)

## Abstract (arXiv)

The Pandora's box problem (Weitzman 1979) is a core model in economic theory that captures an agent's (Pandora's) search for the best alternative (box). We study an important generalization of the problem where the agent can either fully open boxes for a certain fee to reveal their exact values or partially open them at a reduced cost. This introduces a new tradeoff between information acquisition and cost efficiency. We establish a hardness result and employ an array of techniques in stochastic optimization to provide a comprehensive analysis of this model. This includes (1) the identification of structural properties of the optimal policy that provide insights about optimal decisions; (2) the derivation of problem relaxations and provably near-optimal solutions; (3) the characterization of the optimal policy in special yet non-trivial cases; and (4) an extensive numerical study that compares the performance of various policies, and which provides additional insights about the optimal policy. Throughout, we show that intuitive threshold-based policies that extend the Pandora's box optimal solution can effectively guide search decisions.