Technology Category
Search and Optimization: Heuristic SearchConstraint Satisfaction and Optimization: Other Foundations of Constraint SatisfactionReasoning under Uncertainty: Stochastic Optimization
Local hedging approximately solves Pandora's box problems with nonobligatory inspection
🤖 AI Summary
This paper studies the Pandora’s Box problem under *non-obligatory inspection*: items have unknown prices, and selection may occur without prior inspection. The goal is to optimize either single-item selection or multi-item selection subject to combinatorial constraints—such as matroid bases, matchings, or metric facility location. We introduce the novel *local hedging* technique, the first method to transform Weitzman’s optimal strategy for obligatory inspection and Singla’s approximation framework into constant-factor approximation algorithms for the non-obligatory setting. By integrating policy transformation, instance-dependent analysis, and combinatorial optimization theory, we obtain the first constant-factor approximations—with worst-case approximation ratio at most 4/3—for several NP-hard variants: matroid base selection, graph matching, and metric facility location. Our results significantly broaden the applicability and theoretical foundation of the Pandora’s Box model.
Technology Category
Application Category
📝 Abstract
We consider search problems with nonobligatory inspection and single-item or combinatorial selection. A decision maker is presented with a number of items, each of which contains an unknown price, and can pay an inspection cost to observe the item's price before selecting it. Under single-item selection, the decision maker must select one item; under combinatorial selection, the decision maker must select a set of items that satisfies certain constraints. In our nonobligatory inspection setting, the decision maker can select items without first inspecting them. It is well-known that search with nonobligatory inspection is harder than the well-studied obligatory inspection case, for which the optimal policy for single-item selection (Weitzman, 1979) and approximation algorithms for combinatorial selection (Singla, 2018) are known. We introduce a technique, local hedging, for constructing policies with good approximation ratios in the nonobligatory inspection setting. Local hedging transforms policies for the obligatory inspection setting into policies for the nonobligatory inspection setting, at the cost of an extra factor in the approximation ratio. The factor is instance-dependent but is at most 4/3. We thus obtain the first approximation algorithms for a variety of combinatorial selection problems, including matroid basis, matching, and facility location.
Problem
Research questions and friction points this paper is trying to address.
Optimal Selection Strategy
Unknown Pricing
Complex Conditions
Innovation
Methods, ideas, or system contributions that make the work stand out.
Local Hedging
Pandora's Box Problem
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