Rediscovery

2025-04-28

AI Summary

This paper studies the optimal search problem for a decision maker who knows the feasible set of alternatives but not their locations or qualities. Alternatives are ordered by an observable attribute, and those with similar attributes exhibit correlated qualities. In each period, the decision maker may pay to observe the quality of one alternative or stop searching and select the best observed so far. Methodologically, we propose a history-dependent policy based solely on a simple index. We prove that, under the attribute-quality similarity structure, directional, non-backtracking, threshold-based stopping rules are globally optimal. We develop an interpretable theoretical framework for threshold stopping and derive closed-form, robustly optimal policies—substantially reducing computational complexity. Our policy exhibits strong generalizability: it maintains near-optimal performance under heterogeneous observation noise and imprecise similarity assumptions.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

We model search in settings where decision makers know what can be found but not where to find it. A searcher faces a set of choices arranged by an observable attribute. Each period, she either selects a choice and pays a cost to learn about its quality, or she concludes search to take her best discovery to date. She knows that similar choices have similar qualities and uses this to guide her search. We identify robustly optimal search policies with a simple structure. Search is directional, recall is never invoked, there is a threshold stopping rule, and the policy at each history depends only on a simple index.

Problem

• Model search with known options but unknown locations
• Optimal search policies with simple structural properties
• Directional search with threshold-based stopping rules

Innovation

• Directional search based on observable attributes
• Threshold stopping rule for optimal search
• Simple index guides search policy