A1022
Title: Stochastic optimization algorithms for instrumental variable regression with streaming data
Authors: Abhishek Roy - Texas A&M University (United States) [presenting]
Xuxing Chen - Meta (United States)
Yifan Hu - Rutgers Univeristy (United States)
Krishnakumar Balasubramanian - University of California, Davis (United States)
Abstract: The aim is to develop and analyze algorithms for instrumental variable regression by viewing the problem as a conditional stochastic optimization problem. In the context of least-squares instrumental variable regression, the algorithms neither require matrix inversions nor mini-batches, thereby providing a fully online approach for performing instrumental variable regression with streaming data. When the true model is linear, rates of convergence in expectation are derived that are of order $O(\log T/T)$ and $O\left(1/T^{1-\epsilon}\right)$ for any $\epsilon>0$, respectively under the availability of two-sample and one-sample oracles, respectively. Importantly, under the availability of the two-sample oracle, the aforementioned rate is actually agnostic to the relationship between the confounder and the instrumental variable, demonstrating the flexibility of the proposed approach in alleviating the need for explicit model assumptions required in recent works based on reformulating the problem as min-max optimization problems. Experimental validation is provided to demonstrate the advantages of the proposed algorithms over classical approaches like the 2SLS method.
