Similarly to [6], we consider that all environments have the same underlying Structural Causal Model (SCM) and that the different environments correspond to different interventions on the SCM. We provide here the formal definition for SCMs and interventions. We say that Xi causes Xj if Xi 2Pa(Xj). Definition A.2. (Intervention) [6]: Consider a SCMC =( S,N). An intervention e on C consists of replacing one or several of its structural equations to obtain an intervened SCMCe =( Se,N e) with structural equations: Sej: Xej fj(Pa(Xej),N ej), for j =1,...m (11) The variable Xe is intervened on if Si 6= Sei or Ni 6= Nei .

Many real-world domains require safe decision making in uncertain environments. In this work, we introduce a deep reinforcement learning framework for approaching this important problem. We consider a distribution over transition models, and apply a risk-averse perspective towards model uncertainty through the use of coherent distortion risk measures. We provide robustness guarantees for this framework by showing it is equivalent to a specific class of distributionally robust safe reinforcement learning problems. Unlike existing approaches to robustness in deep reinforcement learning, however, our formulation does not involve minimax optimization. This leads to an efficient, model-free implementation of our approach that only requires standard data collection from a single training environment. In experiments on continuous control tasks with safety constraints, we demonstrate that our framework produces robust performance and safety at deployment time across a range of perturbed test environments.

Our design policy successfully achieves amortized intervention design on the distribution of the training environment while also generalizing well to distribution shifts in test-time design environments.