  Rapid advancements in deep learning have led to many recent breakthroughs.
While deep learning models achieve superior performance, often statistically
better than humans, their adoption into safety-critical settings, such as
healthcare or self-driving cars is hindered by their inability to provide
safety guarantees or to expose the inner workings of the model in a human
understandable form. We present Mo\"ET, a novel model based on Mixture of
Experts, consisting of decision tree experts and a generalized linear model
gating function. Thanks to such gating function the model is more expressive
than the standard decision tree. To support non-differentiable decision trees
as experts, we formulate a novel training procedure. In addition, we introduce
a hard thresholding version, Mo\"ETH, in which predictions are made solely by a
single expert chosen via the gating function. Thanks to that property, Mo\"ETH
allows each prediction to be easily decomposed into a set of logical rules in a
form which can be easily verified. While Mo\"ET is a general use model, we
illustrate its power in the reinforcement learning setting. By training Mo\"ET
models using an imitation learning procedure on deep RL agents we outperform
the previous state-of-the-art technique based on decision trees while
preserving the verifiability of the models. Moreover, we show that Mo\"ET can
also be used in real-world supervised problems on which it outperforms other
verifiable machine learning models.
