Data-Driven Synthesis of Probabilistic Controlled Invariant Sets for Linear MDPs
This work addresses safety assurance in reinforcement learning for applications like autonomous systems, though it is incremental as it builds on existing methods for linear MDPs.
The paper tackles the problem of computing probabilistic controlled invariant sets for safety-critical reinforcement learning under unknown dynamics, using a data-driven approach to construct conservative estimates of safe states and actions with confidence guarantees.
We study data-driven computation of probabilistic controlled invariant sets (PCIS) for safety-critical reinforcement learning under unknown dynamics. Assuming a linear MDP model, we use regularized least squares and self-normalized confidence bounds to construct a conservative estimate of the states from which the system can be kept inside a prescribed safe region over an \(N\)-step horizon, together with the corresponding set-valued safe action map. This construction is obtained through a backward recursion and can be interpreted as a conservative approximation of the \(N\)-step safety predecessor operator. When the associated conservative-inclusion event holds, a conservative fixed point of the approximate recursion can be certified as an \((N,ε)\)-PCIS with confidence at least \(η\). For continuous state spaces, we introduce a lattice abstraction and a Lipschitz-based discretization error bound to obtain a tractable approximation scheme. Finally, we use the resulting conservative fixed-point approximation as a runtime candidate PCIS in a practical shielding architecture with iterative updates, and illustrate the approach on a numerical experiment.