Experimentation Under Non-stationary Interference

TL;DR

This paper investigates estimating average treatment effects in randomized trials with evolving interference structures, providing a new estimator with vanishing mean squared error under dynamic, non-stationary interference graphs.

Contribution

It introduces a truncated Horvitz-Thompson estimator for non-stationary interference, with theoretical guarantees and covariance bounds that decay exponentially over time.

Findings

Estimator's MSE vanishes linearly with spatial and temporal blocks

Covariance bounds decay exponentially with time since last interaction

Applicable to dynamic metric space and Erdos-Renyi interference models

Abstract

We study the estimation of the ATE in randomized controlled trials under a dynamically evolving interference structure. This setting arises in applications such as ride-sharing, where drivers move over time, and social networks, where connections continuously form and dissolve. In particular, we focus on scenarios where outcomes exhibit spatio-temporal interference driven by a sequence of random interference graphs that evolve independently of the treatment assignment. Loosely, our main result states that a truncated Horvitz-Thompson estimator achieves an MSE that vanishes linearly in the number of spatial and time blocks, times a factor that measures the average complexity of the interference graphs. As a key technical contribution that contrasts the static setting we present a fine-grained covariance bound for each pair of space-time points that decays exponentially with the time elapsed since their last ``interaction''. Our results can be applied to many concrete settings and lead to simplified bounds, including where the interference graphs (i) are induced by moving points in a metric space, or (ii) follow a dynamic Erdos-Renyi model, where each edge is created or removed independently in each time period.