Pandora with Inaccurate Priors

TL;DR

This paper examines how small inaccuracies in prior knowledge of distributions impact the performance of algorithms solving Pandora's box problem, highlighting the robustness and limitations of existing solutions.

Contribution

It analyzes the effects of distributional errors on the optimal Pandora's box algorithms, providing insights into their robustness under inaccurate priors.

Findings

Inaccurate priors can significantly affect the expected utility of algorithms.

Small errors in distributional knowledge may lead to suboptimal decisions.

The study quantifies the impact of distributional inaccuracies on algorithm performance.

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.