Abstract. Deep reinforcement learning has been successfully applied to many control tasks, but the application of such controllers in safety-critical scenarios has been limited due to safety concerns. Rigorous testing of these controllers is challenging, particularly when they operate in uncertain environments. In this thesis we develop novel verification techniques to give the user stronger guarantees over the performance of the trained agents that they would be able to obtain by testing, under different degrees and sources of uncertainty.

In particular, we tackle three different sources of uncertainty to the agent and offer different algorithms to provide strong guarantees to the user. The first one is input noise: sensors in the real world always provide imperfect data. The second source of uncertainty comes from the actuators: once an agent decides to take a specific action, faulty actuators and or hardware problems could still prevent the agent from acting upon the decisions given by the controller. The last source of uncertainty is the policy: the set of decisions the controller takes when operating in the environment. Agents may act probabilistically for a number of reasons, such as dealing with adversaries in a competitive environment or addressing partial observability of the environment.

In this thesis, we develop formal models of controllers executing under uncertainty, and propose new verification techniques based on abstract interpretation for their analysis. We cover different horizon lengths, i.e., the number of steps into the future that we analyse, and present methods for both finite-horizon and infinite-horizon verification. We perform both probabilistic and non-probabilistic analysis of the models constructed, depending on the methodology adopted. We implement and evaluate our methods on controllers trained for several benchmark control problems.