The desire to use reinforcement learning in safety-critical settings has inspired a recent interest in formal methods for learning algorithms. Existing formal methods for learning and optimization primarily consider the problem of constrained learning or constrained optimization. Given a single correct model and associated safety constraint, these approaches guarantee efficient learning while provably avoiding behaviors outside the safety constraint. Acting well given an accurate environmental model is an important pre-requisite for safe learning, but is ultimately insufficient for systems that operate in complex heterogeneous environments. This paper introduces verification-preserving model updates, the first approach toward obtaining formal safety guarantees for reinforcement learning in settings where multiple possible environmental models must be taken into account. Through a combination of inductive data and deductive proving with design-time model updates and runtime model falsification, we provide a first approach toward obtaining formal safety proofs for autonomous systems acting in heterogeneous environments.
@cite_5: Safe Reinforcement Learning can be defined as the process of learning policies that maximize the expectation of the return in problems in which it is important to ensure reasonable system performance and or respect safety constraints during the learning and or deployment processes. We categorize and analyze two approaches of Safe Reinforcement Learning. The first is based on the modification of the optimality criterion, the classic discounted finite infinite horizon, with a safety factor. The second is based on the modification of the exploration process through the incorporation of external knowledge or the guidance of a risk metric. We use the proposed classification to survey the existing literature, as well as suggesting future directions for Safe Reinforcement Learning.
@cite_27: We consider controller synthesis for stochastic and partially unknown environments in which safety is essential. Specifically, we abstract the problem as a Markov decision process in which the expected performance is measured using a cost function that is unknown prior to run-time exploration of the state space. Standard learning approaches synthesize cost-optimal strategies without guaranteeing safety properties. To remedy this, we first compute safe, permissive strategies. Then, exploration is constrained to these strategies and thereby meets the imposed safety requirements. Exploiting an iterative learning procedure, the resulting strategy is safety-constrained and optimal. We show correctness and completeness of the method and discuss the use of several heuristics to increase its scalability. Finally, we demonstrate the applicability by means of a prototype implementation.
Our approach toward safe reinforcement learning differs from existing approaches that do not include a formal verification component (e.g., as surveyed by Garc ' i a and Fern ' a ndez @cite_5 and the SMT-based constrained learning approach of @cite_27 ) because we focused on safe learning; i.e., instead of relying on oracles or conjectures, constraints are derived in a provably correct way from formally verified safety proofs. The difference between verifiably safe learning and safe learning is significant, and is equivalent to the difference between verified and unverified software. Unlike most existing approaches our safety guarantees apply to both the learning process and the final learned policy.