In multi-armed bandits with network interference (MABNI), the action taken by one node can influence the rewards of others, creating complex interdependence. While existing research on MABNI largely concentrates on minimizing regret, it often overlooks the crucial concern that an excessive emphasis on the optimal arm can undermine the inference accuracy for sub-optimal arms. Although initial efforts have been made to address this trade-off in single-unit scenarios, these challenges have become more pronounced in the context of MABNI. In this paper, we establish, for the first time, a theoretical Pareto frontier characterizing the trade-off between regret minimization and inference accuracy in adversarial (design-based) MABNI. We further introduce an anytime-valid asymptotic confidence sequence along with a corresponding algorithm, $\texttt{EXP3-N-CS}$, specifically designed to balance the trade-off between regret minimization and inference accuracy in this setting.

Estimating causal effects on networks is important for both scientific research and practical applications. Unlike traditional settings that assume the Stable Unit Treatment Value Assumption (SUTVA), interference allows an intervention/treatment on one unit to affect the outcomes of others. Understanding both direct and spillover effects is critical in fields such as epidemiology, political science, and economics. Causal inference on networks faces two main challenges. First, causal effects are typically heterogeneous, varying with unit features and local network structure. Second, connected units often exhibit dependence due to network homophily, creating confounding between structural correlations and causal effects. In this paper, we propose a two-stage method to estimate heterogeneous direct and spillover effects on networks. The first stage uses graph neural networks to estimate nuisance components that depend on the complex network topology. In the second stage, we adjust for network confounding using these estimates and infer causal effects through a novel attention-based interference model. Our approach balances expressiveness and interpretability, enabling downstream tasks such as identifying influential neighborhoods and recovering the sign of spillover effects. We integrate the two stages using Neyman orthogonalization and cross-fitting, which ensures that errors from nuisance estimation contribute only at higher order. As a result, our causal effect estimates are robust to bias and misspecification in modeling causal effects under network dependencies.

Uplift modeling is a key technique for promotion optimization in recommender systems, but standard methods typically fail to account for interference, where treating one item affects the outcomes of others. This violation of the Stable Unit Treatment Value Assumption (SUTVA) leads to suboptimal policies in real-world marketplaces. Recent developments in interference-aware estimators such as Additive Inverse Propensity Weighting (AddIPW) have not found their way into the uplift modeling literature yet, and optimising policies using these estimators is not well-established. This paper proposes a practical methodology to bridge this gap. We use the AddIPW estimator as a differentiable learning objective suitable for gradient-based optimization. We demonstrate how this framework can be integrated with proven response transformation techniques to directly optimize for economic outcomes like incremental profit. Through simulations, we show that our approach significantly outperforms interference-naive methods, especially as interference effects grow. Furthermore, we find that adapting profit-centric uplift strategies within our framework can yield superior performance in identifying the highest-impact interventions, offering a practical path toward more profitable incentive personalization.

All existing approaches require at least approximate knowledge of the network, which may be unavailable or costly to collect.

Many interventions, such as vaccines in clinical trials or coupons in online marketplaces, must be assigned sequentially without full knowledge of their effects. Multi-armed bandit algorithms have proven successful in such settings. However, standard independence assumptions fail when the treatment status of one individual impacts the outcomes of others, a phenomenon known as interference. We study optimal-policy learning under interference on a dynamic network. Existing approaches to this problem require repeated observations of the same fixed network and struggle to scale in sample size beyond as few as fifteen connected units -- both limit applications. We show that under common assumptions on the structure of interference, rewards become linear. This enables us to develop a scalable Thompson sampling algorithm that maximizes policy impact when a new $n$-node network is observed each round. We prove a Bayesian regret bound that is sublinear in $n$ and the number of rounds. Simulation experiments show that our algorithm learns quickly and outperforms existing methods. The results close a key scalability gap between causal inference methods for interference and practical bandit algorithms, enabling policy optimization in large-scale networked systems.