The Power of Adaptivity for Stochastic Submodular Cover

TL;DR

This paper investigates the tradeoffs between the number of adaptive rounds and solution quality in stochastic submodular cover problems, showing that few rounds of adaptivity can approximate fully adaptive solutions effectively.

Contribution

It provides nearly tight bounds on how limited adaptivity affects solution quality, offering practical insights into designing efficient adaptive algorithms.

Findings

Few adaptive rounds suffice to approximate fully adaptive solutions.

Experimental results show near-optimal solutions with limited adaptivity.

Tradeoffs between adaptivity and solution quality are quantitatively characterized.

Abstract

In the stochastic submodular cover problem, the goal is to select a subset of stochastic items of minimum expected cost to cover a submodular function. Solutions in this setting correspond to sequential decision processes that select items one by one "adaptively" (depending on prior observations). While such adaptive solutions achieve the best objective, the inherently sequential nature makes them undesirable in many applications. We ask: how well can solutions with only a few adaptive rounds approximate fully-adaptive solutions? We give nearly tight answers for both independent and correlated settings, proving smooth tradeoffs between the number of adaptive rounds and the solution quality, relative to fully adaptive solutions. Experiments on synthetic and real datasets show qualitative improvements in the solutions as we allow more rounds of adaptivity; in practice, solutions with a few rounds of adaptivity are nearly as good as fully adaptive solutions.