  This paper proposes a novel approach for constructing effective personalized
policies when the observed data lacks counter-factual information, is biased
and possesses many features. The approach is applicable in a wide variety of
settings from healthcare to advertising to education to finance. These settings
have in common that the decision maker can observe, for each previous instance,
an array of features of the instance, the action taken in that instance, and
the reward realized -- but not the rewards of actions that were not taken: the
counterfactual information. Learning in such settings is made even more
difficult because the observed data is typically biased by the existing policy
(that generated the data) and because the array of features that might affect
the reward in a particular instance -- and hence should be taken into account
in deciding on an action in each particular instance -- is often vast. The
approach presented here estimates propensity scores for the observed data,
infers counterfactuals, identifies a (relatively small) number of features that
are (most) relevant for each possible action and instance, and prescribes a
policy to be followed. Comparison of the proposed algorithm against the
state-of-art algorithm on actual datasets demonstrates that the proposed
algorithm achieves a significant improvement in performance.
