Fast and Robust Online Inference with Stochastic Gradient Descent via Random Scaling
This provides a robust and efficient online inference method for large-scale data applications, though it is incremental as it builds on existing SGD and econometric techniques.
The paper tackles the problem of online inference for parameters estimated by SGD with Polyak-Ruppert averaging, developing a method that uses random scaling to construct asymptotically pivotal statistics, which is shown to be robust to tuning parameter changes in simulations.
We develop a new method of online inference for a vector of parameters estimated by the Polyak-Ruppert averaging procedure of stochastic gradient descent (SGD) algorithms. We leverage insights from time series regression in econometrics and construct asymptotically pivotal statistics via random scaling. Our approach is fully operational with online data and is rigorously underpinned by a functional central limit theorem. Our proposed inference method has a couple of key advantages over the existing methods. First, the test statistic is computed in an online fashion with only SGD iterates and the critical values can be obtained without any resampling methods, thereby allowing for efficient implementation suitable for massive online data. Second, there is no need to estimate the asymptotic variance and our inference method is shown to be robust to changes in the tuning parameters for SGD algorithms in simulation experiments with synthetic data.