Endogeneity, i.e. the dependence between noise and covariates, is a common phenomenon in real data due to omitted variables, strategic behaviours, measurement errors etc. In contrast, the existing analyses of stochastic online linear regression with unbounded noise and linear bandits depend heavily on exogeneity, i.e. the independence between noise and covariates. Motivated by this gap, we study the over-and just-identified Instrumental Variable (IV) regression for stochastic online learning. IV regression and the Two-Stage Least Squares approach to it are widely deployed in economics and causal inference to identify the underlying model from an endogenous dataset. Thus, we propose to use an online variant of Two-Stage Least Squares approach, namely O2SLS, to tackle endogeneity in stochastic online learning. Our analysis shows that O2SLS achieves $\mathcal{O}\left(d_x d_z \log ^2 T\right)$ identification and $\tilde{\mathcal{O}}\left(\gamma \sqrt{d_x T}\right)$ oracle regret after $T$ interactions, where $d_x$ and $d_z$ are the dimensions of covariates and IVs, and $\gamma$ is the bias due to endogeneity. For $\gamma=0$, i.e. under exogeneity, O2SLS achieves $\mathcal{O}\left(d_x^2 \log ^2 T\right)$ oracle regret, which is of the same order as that of the stochastic online ridge. Then, we leverage O2SLS as an oracle to design OFUL-IV, a stochastic linear bandit algorithm that can tackle endogeneity and achieves $\widetilde{\mathcal{O}}\left(\sqrt{d_x d_z T}\right)$ regret. For different datasets with endogeneity, we experimentally show efficiencies of O2SLS and OFUL-IV in terms of regrets.

We postulate that the nature of information items plays a vital role in the observed spread of these items in a social network. We capture this intuition by proposing a model that assigns to every information item two parameters: endogeneity and exogeneity. The endogeneity of the item quantifies its tendency to spread primarily through the connections between nodes; the exogeneity quantifies its tendency to be acquired by the nodes, independently of the underlying network. We also extend this item-based model to take into account the openness of each node to new information. We quantify openness by introducing the receptivity of a node. Given a social network and data related to the ordering of adoption of information items by nodes, we develop a maximum-likelihood framework for estimating endogeneity, exogeneity and receptivity parameters. We apply our methodology to synthetic and real data and demonstrate its efficacy as a data-analytic tool.