  Policy learning utilizing observational data is pivotal across various
domains, with the objective of learning the optimal treatment assignment policy
while adhering to specific constraints such as fairness, budget, and
simplicity. This study introduces a novel positivity-free (stochastic) policy
learning framework designed to address the challenges posed by the
impracticality of the positivity assumption in real-world scenarios. This
framework leverages incremental propensity score policies to adjust propensity
score values instead of assigning fixed values to treatments. We characterize
these incremental propensity score policies and establish identification
conditions, employing semiparametric efficiency theory to propose efficient
estimators capable of achieving rapid convergence rates, even when integrated
with advanced machine learning algorithms. This paper provides a thorough
exploration of the theoretical guarantees associated with policy learning and
validates the proposed framework's finite-sample performance through
comprehensive numerical experiments, ensuring the identification of causal
effects from observational data is both robust and reliable.
