Policy design in experiments with unknown interference

Davide Viviano; Jess Rudder

econ.EMNov 16, 2020

Policy design in experiments with unknown interference

Authors: Davide Viviano, Jess Rudder

Organizations: Department of Economics, Harvard University, 1805 Cambridge St, Cambridge, MA 02138. · Department of Economics, Oregon State University, 1500 SW Jefferson Way, Corvallis, OR 97331.

Abstract

This paper studies experimental designs for estimation and inference on policies with spillover effects. Units are organized into a finite number of large clusters and interact in unknown ways within each cluster. First, we introduce a single-wave experiment that, by varying the randomization across cluster pairs, estimates the marginal effect of a change in treatment probabilities, taking spillover effects into account. Using the marginal effect, we propose a test for policy optimality. Second, we design a multiple-wave experiment to estimate welfare-maximizing treatment rules. We provide strong theoretical guarantees and an implementation in a large-scale field experiment.

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Adaptive Policy Learning Under Unknown Network Interference

Aidan Gleich, Eric Laber, Alexander Volfovsky

Department of Statistical Science Duke University

Adaptive experimentation under unknown network interference requires solving two coupled problems: (i) learning the underlying dynamics of interference among units and (ii) using these dynamics to inform treatment allocation in order to maximize a cumulative outcome of interest (e.g. revenue). Existing adaptive experimentation methods either assume the interference network is fully known or bypass the network by operating on coarse cluster-level randomizations. We develop a Thompson sampling algorithm that jointly learns the interference network and adaptively optimizes individual-level treatment allocations via a Gibbs sampler. The algorithm returns both an optimized treatment policy and an estimate of the interference network; the latter supports downstream causal analyses such as estimation of direct, indirect, and total treatment effects. For additive spillover models, we show that total reward is linear in the treatment vector with coefficients given by an

n

-dimensional latent score. We prove a Bayesian regret bound of order

\sqrt{nT \cdot B \log(en/B)}

for exact posterior sampling; empirically, our Gibbs-based approximate sampler achieves regret consistent with this rate and remains sublinear when the additive spillovers assumption is violated. For general Neighborhood Interference, where this reduction is unavailable, we analyze an explore-then-commit variant with

O(n^2 \log T)

graph-discovery cost. An information-theoretic

Ω(n \log T)

lower bound complements both results. Empirically, our method achieves more than an order-of-magnitude reduction in regret in head-to-head comparisons. On two real-world networks, the algorithm achieves sublinear regret and yields downstream effect estimates with small RMSE relative to the truth.

Thompson Sampling Treatment Effect Interference Optimal Policies

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Abstract

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