  Because different patients may response quite differently to the same drug or
treatment, there is increasing interest in discovering individualized treatment
rule. In particular, people are eager to find the optimal individualized
treatment rules, which if followed by the whole patient population would lead
to the "best" outcome. In this paper, we propose new estimators based on robust
regression with general loss functions to estimate the optimal individualized
treatment rules. The new estimators possess the following nice properties:
first, they are robust against skewed, heterogeneous, heavy-tailed errors or
outliers; second, they are robust against misspecification of the baseline
function; third, under certain situations, the new estimator coupled with
pinball loss approximately maximizes the outcome's conditional quantile instead
of conditional mean, which leads to a different optimal individualized
treatment rule comparing with traditional Q- and A-learning. Consistency and
asymptotic normality of the proposed estimators are established. Their
empirical performance is demonstrated via extensive simulation studies and an
analysis of an AIDS data.
