In many scientific and engineering domains, inferring the effect of treatment and exploring its heterogeneity is crucial for optimization and decision making. In addition to Machine Learning based models (e.g. Random Forests or Neural Networks), many meta-algorithms have been developed to estimate the Conditional Average Treatment Effect (CATE) function in the binary setting, with the main advantage of not restraining the estimation to a specific supervised learning method. However, this task becomes more challenging when the treatment is not binary. In this paper, we investigate the Rubin Causal Model under the multiple treatment regime and we focus on estimating heterogeneous treatment effects. We generalize Meta-learning algorithms to estimate the CATE for each possible treatment value. Using synthetic and semi-synthetic simulation datasets, we assess the quality of each meta-learner in observational data, and we highlight in particular the performances of the X-learner.

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