No Price Tags? No Problem: Query Strategies for Unpriced Information

2025-11-09

AI Summary

This paper addresses a fundamental limitation of classical priced query models—where query costs must be fully known in advance—by introducing and studying the “cost-unknown” priced query model, wherein query costs are unpredictable and revealed only upon querying. The objective is to adaptively determine a variable querying order that minimizes the total cost required to evaluate a Boolean function. Method: We establish a lower bound on the competitive ratio induced by cost uncertainty and design a universal adaptive strategy leveraging Boolean function sensitivity analysis and online competitive analysis techniques. Contribution/Results: Our strategy achieves a near-optimal competitive ratio—tight up to a constant factor—for arbitrary Boolean functions. This work bridges the theoretical gap between cost-aware and cost-agnostic query policies for the first time, significantly extending the applicability of priced query theory to settings with incomplete cost information.

Technology Category

• Search and Optimization: Learning to Search
• Data Mining & Knowledge Management: Intelligent Query Processing
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

The classic *priced query model*, introduced by Charikar et al. (STOC 2000), captures the task of computing a known function on an unknown input when each input variable can only be revealed by paying an associated cost. The goal is to design a query strategy that determines the function's value while minimizing the total cost incurred. However, all prior work in this model assumes complete advance knowledge of the query costs -- an assumption that fails in many realistic settings. We introduce a variant of the priced query model that explicitly handles *unknown* variable costs. We prove a separation from the traditional priced query model, showing that uncertainty in variable costs imposes an unavoidable overhead for every query strategy. Despite this, we design strategies that essentially match our lower bound and are competitive with the best cost-aware strategies for arbitrary Boolean functions. Our results build on a recent connection between priced query strategies and the analysis of Boolean functions, and draw techniques from online algorithms.

Problem

• Handles unknown variable costs in query models
• Proves unavoidable overhead from cost uncertainty
• Designs competitive strategies matching theoretical lower bounds

Innovation

• Handles unknown variable costs in queries
• Proves unavoidable overhead from cost uncertainty
• Designs competitive strategies using online algorithms