Trustworthy machine learning aims at combating distributional uncertainties in training data distributions compared to population distributions. Typical treatment frameworks include the Bayesian approach, (min-max) distributionally robust optimization (DRO), and regularization. However, two issues have to be raised: 1) All these methods are biased estimators of the true optimal cost; 2) the prior distribution in the Bayesian method, the radius of the distributional ball in the DRO method, and the regularizer in the regularization method are difficult to specify. This paper studies a new framework that unifies the three approaches and that addresses the two challenges mentioned above. The asymptotic properties (e.g., consistency and asymptotic normalities), non-asymptotic properties (e.g., unbiasedness and generalization error bound), and a Monte--Carlo-based solution method of the proposed model are studied. The new model reveals the trade-off between the robustness to the unseen data and the specificity to the training data.

Explainability of Reinforcement Learning (RL) policies remains a challenging research problem, particularly when considering RL in a safety context. Understanding the decisions and intentions of an RL policy offer avenues to incorporate safety into the policy by limiting undesirable actions. We propose the use of a Boolean Decision Rules model to create a post-hoc rule-based summary of an agent's policy. We evaluate our proposed approach using a DQN agent trained on an implementation of a lava gridworld and show that, given a hand-crafted feature representation of this gridworld, simple generalised rules can be created, giving a post-hoc explainable summary of the agent's policy. We discuss possible avenues to introduce safety into a RL agent's policy by using rules generated by this rule-based model as constraints imposed on the agent's policy, as well as discuss how creating simple rule summaries of an agent's policy may help in the debugging process of RL agents.