In this supplementary material, we describe in details the simulation procedures including all parameters, additional model fitting details, and additional simulation results for section 4.1 in the main In this section, we describe the data generating mechanism in section 4.1 of the main paper. In order to learn the three latent domains in the correct directions, we control the direction of the estimated parameters for one item per latent domain. Table A.1: Simulation parameters for the conditional distributions of observed items Table B.1: Accuracy of the fitted optimal treatment on the test set from 100 simulations for training sample size of 200, 500, 1000, and 2000