  Causal inference methods are widely applied in various decision-making
domains such as precision medicine, optimal policy and economics. Central to
these applications is the treatment effect estimation of intervention
strategies. Current estimation methods are mostly restricted to the
deterministic treatment, which however, is unable to address the stochastic
space treatment policies. Moreover, previous methods can only make binary
yes-or-no decisions based on the treatment effect, lacking the capability of
providing fine-grained effect estimation degree to explain the process of
decision making. In our study, we therefore advance the causal inference
research to estimate stochastic intervention effect by devising a new
stochastic propensity score and stochastic intervention effect estimator (SIE).
Meanwhile, we design a customized genetic algorithm specific to stochastic
intervention effect (Ge-SIO) with the aim of providing causal evidence for
decision making. We provide the theoretical analysis and conduct an empirical
study to justify that our proposed measures and algorithms can achieve a
significant performance lift in comparison with state-of-the-art baselines.
