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

We discuss the results on improving the generalizability of individualized treatment rule following the work in Kallus [1] and Mo et al. [5]. We note that the advocated weights in Kallus [1] 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 in Mo et al. [5]. 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.