Off-Policy Reinforcement Learning with Anytime Safety Guarantees via Robust Safe Gradient Flow

Abstract: This paper considers the problem of solving constrained reinforcement learning (RL) problems with anytime guarantees, meaning that the algorithmic solution must yield a constraint-satisfying policy at every iteration of its evolution. Our design is based on a discretization of the Robust Safe Gradient Flow (RSGF), a continuous-time dynamics for anytime constrained optimization whose forward invariance and stability properties we formally characterize. The proposed strategy, termed RSGF-RL, is an off-policy algorithm which uses episodic data to estimate the value functions and their gradients and updates the policy parameters by solving a convex quadratically constrained quadratic program. Our technical analysis combines statistical analysis, the theory of stochastic approximation, and convex analysis to determine the number of episodes sufficient to ensure that safe policies are updated to safe policies and to recover from an unsafe policy, both with an arbitrary user-specified probability, and to establish the asymptotic convergence to the set of KKT points of the RL problem almost surely. Simulations on a navigation example and the cart-pole system illustrate the superior performance of RSGF-RL with respect to the state of the art.