Near-Optimal Experimental Design for Networks: Independent Block Randomization

68 Pages Posted: 1 Jun 2021 Last revised: 30 Sep 2021

See all articles by Ozan Candogan

Ozan Candogan

University of Chicago - Booth School of Business

Chen Chen

University of Chicago - Booth School of Business

Rad Niazadeh

University of Chicago - Booth School of Business

Date Written: May 24, 2021

Abstract

Motivated by the prevalence of experimentation in online platforms and social networks, we consider the problem of designing randomized experiments to assess the effectiveness of a new market intervention for a network of users. An experiment assigns each user to either the treatment or the control group. The outcome of each user depends on her assignment as well as the assignments of her neighbors. Given the experiment, the unbiased Horvitz-Thompson estimator is used to estimate the total market effect of the treatment. The decision maker chooses randomized assignments of users to treatment and control, in order to minimize the worst-case variance of this estimator. We focus on networks that can be partitioned into communities, where the users in the same community are densely connected, and users from different communities are only loosely connected. In such settings, it is almost without loss to assign all users in the same community to the same variant (treatment or control). The problem of designing the optimal randomized assignments of communities can be formulated as a linear program with an exponential number of decision variables and constraints in the number of communities---and hence, is generally computationally intractable.

We develop a family of practical experiments that we refer to as \emph{independent block randomization (IBR)} experiments. Such an experiment partitions communities into blocks so that each block contains communities of similar sizes. It then treats half of the communities in each block (chosen uniformly at random) and does so independently across blocks. The optimal community partition can be obtained in a tractable way using dynamic programming. We show that these policies are asymptotically optimal when the number of communities grows large and no community size dominates the rest. In the special case where community sizes take values in a finite set and the number of communities of each size is a fixed proportion of the total number of communities, the loss is only a constant that is independent of the number of communities. Beyond the asymptotic regime, we show that the IBR experiment is a 7/3-approximation for any problem instance. We also examine the performance of the IBR experiments on data-driven numerical examples, including examples based on Facebook subnetworks.

Keywords: Experimental design, cluster-based randomization, social networks, interference, approximation algorithms, asymptotic optimality.

Suggested Citation

Candogan, Ozan and Chen, Chen and Niazadeh, Rad, Near-Optimal Experimental Design for Networks: Independent Block Randomization (May 24, 2021). Chicago Booth Research Paper No. 21-17, Available at SSRN: https://ssrn.com/abstract=3852100 or http://dx.doi.org/10.2139/ssrn.3852100

Ozan Candogan

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States

HOME PAGE: http://faculty.chicagobooth.edu/ozan.candogan/

Chen Chen (Contact Author)

University of Chicago - Booth School of Business ( email )

5807 S Woodlawn Ave
Chicago, IL 60637
United States

Rad Niazadeh

University of Chicago - Booth School of Business ( email )

5807 S Woodlawn Ave
Chicago, IL 60637

HOME PAGE: http://radniazadeh.github.io/

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