Reachability Constrained Reinforcement Learning

Constrained Reinforcement Learning (CRL) has gained significant interest recently, since the satisfaction of safety constraints is critical for real world problems. However, existing CRL methods constraining discounted cumulative costs generally lack rigorous definition and guarantee of safety. On the other hand, in the safe control research, safety is defined as persistently satisfying certain state constraints. Such persistent safety is possible only on a subset of the state space, called feasible set, where an optimal largest feasible set exists for a given environment. Recent studies incorporating safe control with CRL using energy-based methods such as control barrier function (CBF), safety index (SI) leverage prior conservative estimation of feasible sets, which harms performance of the learned policy. To deal with this problem, this paper proposes a reachability CRL (RCRL) method by using reachability analysis to characterize the largest feasible sets. We characterize the feasible set by the established self-consistency condition, then a safety value function can be learned and used as constraints in CRL. We also use the multi-time scale stochastic approximation theory to prove that the proposed algorithm converges to a local optimum, where the largest feasible set can be guaranteed. Empirical results on different benchmarks such as safe-control-gym and Safety-Gym validate the learned feasible set, the performance in optimal criteria, and constraint satisfaction of RCRL, compared to state-of-the-art CRL baselines.