Action selection in growing state spaces: Control of Network Structure Growth

TL;DR

This paper presents a stochastic optimal control framework to influence the growth of network structures, aiming to shape their topology for desired dynamical behaviors, demonstrated through conversation thread formation.

Contribution

It introduces a novel control approach using probabilistic inference and adaptive importance sampling to steer network growth towards desired topologies.

Findings

Controlled conversation threads have improved structural properties.

The method effectively influences network growth in realistic models.

Adaptive sampling enhances control accuracy in high-dimensional settings.

Abstract

The dynamical processes taking place on a network depend on its topology. Influencing the growth process of a network therefore has important implications on such dynamical processes. We formulate the problem of influencing the growth of a network as a stochastic optimal control problem in which a structural cost function penalizes undesired topologies. We approximate this control problem with a restricted class of control problems that can be solved using probabilistic inference methods. To deal with the increasing problem dimensionality, we introduce an adaptive importance sampling method for approximating the optimal control. We illustrate this methodology in the context of formation of information cascades, considering the task of influencing the structure of a growing conversation thread, as in Internet forums. Using a realistic model of growing trees, we show that our approach can yield conversation threads with better structural properties than the ones observed without control.