Online Instrumental Variable Regression with Applications to Online Linear System Identification

Instrumental variable regression (IVR) is a statistical technique utilized for recovering unbiased estimators when there are errors in the independent variables. Estimator bias in learned time series models can yield poor performance in applications such as long-term prediction and filtering where the recursive use of the model results in the accumulation of propagated error. However, prior work addressed the IVR objective in the batch setting, where it is necessary to store the entire dataset in memory an infeasible requirement in large dataset scenarios. In this work, we develop Online Instrumental Variable Regression (OIVR), an algorithm that is capable of updating the learned estimator with streaming data. We show that the online adaptation of IVR enjoys a no-regret performance guarantee with respect the original batch setting by taking advantage of any no-regret online learning algorithm inside OIVR for the underlying update steps. We experimentally demonstrate the efficacy of our algorithm in combination with popular no-regret online algorithms for the task of learning predictive dynamical system models and on a prototypical econometrics instrumental variable regression problem.