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

TL;DR

This paper introduces a new variant of the priced query model that handles unknown variable costs, demonstrating inherent overheads and proposing strategies that are nearly optimal despite cost uncertainty.

Contribution

It extends the classic priced query model to account for unknown costs, establishing lower bounds and designing near-optimal strategies under uncertainty.

Findings

Uncertainty in variable costs causes unavoidable overheads in query strategies.

Proposed strategies nearly match the theoretical lower bounds.

The approach leverages connections to Boolean function analysis and online algorithms.

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.