Safety by Invariance, Liveness through Refinement: Heterogeneous Contract Framework for Co-Design of Layered Control

Safe reinforcement learning (RL) typically asks $\textit{what}$ an agent should do. We ask $\textit{when}$ it needs to act, and show that a single policy can jointly learn control inputs and communication-efficient timing decisions under a pointwise Lyapunov safety shield. We focus on stabilization around a known equilibrium, where CARE-based LQR backups, Lyapunov certificates, and classical Lyapunov-STC are well defined, enabling clean comparison against analytical baselines. A run-time assurance (RTA) layer overrides the policy via a one-step-ahead Lyapunov prediction and a precomputed LQR backup, providing a strictly stronger guarantee than constrained MDP methods that enforce safety only in expectation. On an inverted pendulum, cart--pole, and planar quadrotor, the learned policy achieves $1.91\times$, $1.45\times$, and $3.51\times$ higher mean inter-sample interval (MSI) than a Lyapunov-triggered baseline; a fixed LQR controller at the same average rate is unstable on all three plants, showing that adaptive timing, not a lower average rate, makes sparsity safe. A CARE-derived Lyapunov reward transfers across environments without redesign, with a single weight $w_c$ controlling the stability--communication tradeoff; ablations confirm the RTA shield is essential, with its removal reducing MSI by $1.27$--$1.84\times$ and degrading state norms. A preference-conditioned extension recovers the full tradeoff frontier from one model at $\tfrac{2}{11}$ of training compute, and SAC experiments show the results are algorithm-agnostic across discrete and continuous domains. A 12-state 3D quadrotor case study extends the framework to higher-dimensional systems where classical STC is intractable, and robustness to $\pm30\%$ mass variation and disturbances shows graceful degradation, with the RTA absorbing what the learned policy cannot.

Autonomous systems are increasingly deployed in real-world environments, where they must achieve high performance while maintaining safety under state and input constraints. Although Model Predictive Control (MPC) provides a principled framework for constrained optimal control, guaranteeing safety beyond its finite planning horizon remains a fundamental challenge. In this work, we augment MPC with a safety value function-based terminal constraint that enforces membership in a control-invariant safe set at the end of each planning horizon. This formulation enables real-time synthesis of trajectories that are both high-performing and provably safe. We show that, under an exact safety value function and a feasible initialization, the proposed MPC scheme is recursively feasible, thereby ensuring persistent safety. In contrast to traditional terminal set constructions that rely on local linearizations or conservative approximations, our approach incorporates a reachability-based safety value function for terminal constraints, yielding less conservative and more expressive safety guarantees. We validate the proposed framework through simulation and hardware experiments on a Flexiv Rizon 10s manipulator. Results demonstrate improved constraint satisfaction and robustness compared to standard state-constrained MPC and reactive safety filtering, while maintaining competitive task performance. The full implementation and experiments are available on the project website.

Safety in reinforcement learning is often specified through cumulative cost constraints, but these trajectory-level guarantees do not directly prevent unsafe individual decisions, especially under nonstationarity. In continual and nonstationary settings, the difficulty is amplified because the risk associated with the same action can vary across contexts, while a fixed state-level threshold may be either too conservative or too weak. We propose Constraint Projection Safety Shield (CPSS), a runtime mechanism that converts a cumulative safety budget into adaptive state-level control constraints during execution. CPSS tracks the remaining safety budget, projects it into a time-varying admissible risk threshold, and filters policy actions whose predicted safety cost exceeds the active threshold. The threshold is adjusted online using contextual signals so that enforcement becomes stricter in more demanding or rapidly changing regimes and less restrictive when the available safety budget is sufficient. We analyze the resulting shielded policy and show that the mechanism guarantees per-state threshold satisfaction for executed actions, induces finite-horizon cumulative cost bounds, and yields a performance degradation bound in terms of intervention frequency and per-step reward distortion. We evaluate CPSS in nonstationary highway merging scenarios using highway-env. Across multiple seeds, CPSS substantially reduces proximity-based safety violations and increases separation margins while intervening selectively rather than dominating the learned policy. These results support adaptive budget-to-threshold projection as a practical way to transform cumulative safety specifications into effective local safety control for continual reinforcement learning systems.