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Causal inference methods are widely applied in various decision-making domains such as precision medicine, optimal policy and economics. Central to causal inference is the treatment effect estimation of intervention strategies, such as changes in drug dosing and increases in financial aid. Existing methods are mostly restricted to the deterministic treatment and compare outcomes under different treatments. However, they are unable to address the substantial recent interest of treatment effect estimation under stochastic treatment, e.g., "how all units health status change if they adopt 50% dose reduction". In other words, they lack the capability of providing fine-grained treatment effect estimation to support sound decision-making. In our study, we advance the causal inference research by proposing a new effective framework to estimate the treatment effect on stochastic intervention. Particularly, we develop a stochastic intervention effect estimator (SIE) based on nonparametric influence function, with the theoretical guarantees of robustness and fast convergence rates. Additionally, we construct a customised reinforcement learning algorithm based on the random search solver which can effectively find the optimal policy to produce the greatest expected outcomes for the decision-making process. Finally, we conduct an empirical study to justify that our framework can achieve significant performance in comparison with state-of-the-art baselines.

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Counterfactual explanation is one branch of interpretable machine learning that produces a perturbation sample to change the model's original decision. The generated samples can act as a recommendation for end-users to achieve their desired outputs. Most of the current counterfactual explanation approaches are the gradient-based method, which can only optimize the differentiable loss functions with continuous variables. Accordingly, the gradient-free methods are proposed to handle the categorical variables, which however present several major limitations: 1) causal relationships among features are typically ignored when generating the counterfactuals, possibly resulting in impractical guidelines for decision-makers; 2) the generation of the counterfactual sample is prohibitively slow and requires lots of parameter tuning for combining different loss functions. In this work, we propose a causal structure model to preserve the causal relationship underlying the features of the counterfactual. In addition, we design a novel gradient-free optimization based on the multi-objective genetic algorithm that generates the counterfactual explanations for the mixed-type of continuous and categorical data. Numerical experiments demonstrate that our method compares favorably with state-of-the-art methods and therefore is applicable to any prediction model. All the source code and data are available at https: // github.com/ tridungduong16/ multiobj-scm-cf .

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