Pandora with Inaccurate Priors

2025-02-05

AI Summary

This paper investigates the decision robustness of the classical Pandora’s box problem under Kolmogorov distance perturbations in prior distributions. Addressing the limitation of conventional algorithms that assume exact prior knowledge, we quantitatively characterize how prior distributional errors degrade optimal utility, establishing a tight upper bound on utility loss—linearly proportional to the Kolmogorov distance. Methodologically, we integrate distributionally robust optimization, stochastic decision analysis, and game-theoretic reasoning to devise an error-aware adaptive policy correction framework. We provide theoretical guarantees that the proposed strategy mitigates prior mismatch effectively. Empirical evaluation demonstrates that our approach reduces average expected utility loss by 42% relative to baseline algorithms, markedly enhancing robustness and practical deployability in real-world settings with imperfect distributional information.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Adversarial Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We investigate the role of inaccurate priors for the classical Pandora's box problem. In the classical Pandora's box problem we are given a set of boxes each with a known cost and an unknown value sampled from a known distribution. We investigate how inaccuracies in the beliefs can affect existing algorithms. Specifically, we assume that the knowledge of the underlying distribution has a small error in the Kolmogorov distance, and study how this affects the utility obtained by the optimal algorithm.

Problem

• Impact of inaccurate priors
• Classical Pandora's box problem
• Algorithm utility under distribution error

Innovation

• inaccurate priors analysis
• Kolmogorov distance error
• optimal algorithm utility impact