Discussion of Kallus (2020) and Mo et al. (2020)

We discuss the results on improving the generalizability of individualized treatment rule following the work by Kallus and Mo et al. We note that the advocated weights in the work of Kallus are connected to the efficient score of the contrast function. We further propose a likelihood-ratio-based method (LR-ITR) to accommodate covariate shifts, and compare it to the CTE-DR-ITR method proposed by Mo et al. We provide the upper-bound on the risk function of the target population when both the covariate shift and the contrast function shift are present. Numerical studies show that LR-ITR can outperform CTE-DR-ITR when there is only covariate shift. for this article are available online.