Query Minimization under Stochastic Uncertainty

TL;DR

This paper investigates optimal query strategies under stochastic uncertainty, proposing polynomial-time solutions for sorting and revealing complexity for finding minima, with implications for online decision-making.

Contribution

It introduces an adaptive decision tree approach for stochastic interval queries, showing polynomial-time solutions for sorting and evidence of hardness for minimum finding.

Findings

Polynomial-time decision tree for sorting under stochastic uncertainty.

Evidence of computational hardness for minimum element identification.

Stochastic assumptions enable surpassing traditional approximation bounds in online settings.

Abstract

We study problems with stochastic uncertainty information on intervals for which the precise value can be queried by paying a cost. The goal is to devise an adaptive decision tree to find a correct solution to the problem in consideration while minimizing the expected total query cost. We show that, for the sorting problem, such a decision tree can be found in polynomial time. For the problem of finding the data item with minimum value, we have some evidence for hardness. This contradicts intuition, since the minimum problem is easier both in the online setting with adversarial inputs and in the offline verification setting. However, the stochastic assumption can be leveraged to beat both deterministic and randomized approximation lower bounds for the online setting.