Online statistical inference for parameters estimation with linear-equality constraints

Stochastic gradient descent (SGD) and projected stochastic (PSGD) are scalable algorithms to compute model parameters in unconstrained constrained optimization problems. In comparison with SGD, PSGD forces its iterative values into the parameter space via projection. From a statistical point of view, this paper studies limiting distribution PSGD-based estimate when true satisfy some linear-equality constraints. Our theoretical findings reveal role projection played uncertainty estimate. As byproduct, we propose an online hypothesis testing procedure test Simulation on synthetic data application real-world dataset confirm our theory.