  The individualized treatment rule (ITR), which recommends an optimal
treatment based on individual characteristics, has drawn considerable interest
from many areas such as precision medicine, personalized education, and
personalized marketing. Existing ITR estimation methods mainly adopt one of two
or more treatments. However, a combination of multiple treatments could be more
powerful in various areas. In this paper, we propose a novel Double Encoder
Model (DEM) to estimate the individualized treatment rule for combination
treatments. The proposed double encoder model is a nonparametric model which
not only flexibly incorporates complex treatment effects and interaction
effects among treatments, but also improves estimation efficiency via the
parameter-sharing feature. In addition, we tailor the estimated ITR to budget
constraints through a multi-choice knapsack formulation, which enhances our
proposed method under restricted-resource scenarios. In theory, we provide the
value reduction bound with or without budget constraints, and an improved
convergence rate with respect to the number of treatments under the DEM. Our
simulation studies show that the proposed method outperforms the existing ITR
estimation in various settings. We also demonstrate the superior performance of
the proposed method in PDX data that recommends optimal combination treatments
to shrink the tumor size of the colorectal cancer.
