![MathJax Logo](/templates/jsp/_style2/_tandf/pb2/images/math-jax.gif)
Article title: Statistical Inference for Online Decision Making via Stochastic Gradient Descent
Authors: Haoyu Chen,Wenbin Lu, and Rui Song
Journal: Journal of the American Statistical Association
DOI: 10.1080/01621459.2020.1826325
In Section 4, Assumption A5 should be
A5. The features vector X satisfies . The second moment of reward exists for any given covariates and action, that is,
The only change is the removal of the expectation notation before
in the first sentence. That is, we would require a bound on all realizations of
instead of the expectation of
. The main theorems built upon this assumption and conclusions of the article will remain unchanged.
In the supplement, Section A.3 “Proof of Theorems 4.1 and 4.2”, are modified as follows
Note that under our model setting. By Assumption A5, there exists a constant
such that
. By Cauchy-Schwarz inequality
Then using Assumption A6 we have,